Daily Papers

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via p_θ(y mid x) and, with fixed or absent inputs, unconditional generation via p_θ(x). Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability. https://ahn-ml.github.io/gram-website

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.

Multi-sensor fusion is crucial for improving the performance and robustness of end-to-end autonomous driving systems. Existing methods predominantly adopt either attention-based flatten fusion or bird's eye view fusion through geometric transformations. However, these approaches often suffer from limited interpretability or dense computational overhead. In this paper, we introduce GaussianFusion, a Gaussian-based multi-sensor fusion framework for end-to-end autonomous driving. Our method employs intuitive and compact Gaussian representations as intermediate carriers to aggregate information from diverse sensors. Specifically, we initialize a set of 2D Gaussians uniformly across the driving scene, where each Gaussian is parameterized by physical attributes and equipped with explicit and implicit features. These Gaussians are progressively refined by integrating multi-modal features. The explicit features capture rich semantic and spatial information about the traffic scene, while the implicit features provide complementary cues beneficial for trajectory planning. To fully exploit rich spatial and semantic information in Gaussians, we design a cascade planning head that iteratively refines trajectory predictions through interactions with Gaussians. Extensive experiments on the NAVSIM and Bench2Drive benchmarks demonstrate the effectiveness and robustness of the proposed GaussianFusion framework. The source code will be released at https://github.com/Say2L/GaussianFusion.

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. We extensively evaluate our method on simulated data, demonstrate its effectiveness on downstream applications such as robotics, and show promising accuracy on real-world intuitive physics datasets. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

Recent advances in large language models (LLMs) have sparked growing interest in integrating language-driven techniques into trajectory prediction. By leveraging their semantic and reasoning capabilities, LLMs are reshaping how autonomous systems perceive, model, and predict trajectories. This survey provides a comprehensive overview of this emerging field, categorizing recent work into five directions: (1) Trajectory prediction via language modeling paradigms, (2) Direct trajectory prediction with pretrained language models, (3) Language-guided scene understanding for trajectory prediction, (4) Language-driven data generation for trajectory prediction, (5) Language-based reasoning and interpretability for trajectory prediction. For each, we analyze representative methods, highlight core design choices, and identify open challenges. This survey bridges natural language processing and trajectory prediction, offering a unified perspective on how language can enrich trajectory prediction.

Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-of-the-art deterministic and generative methods.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

Maritime vessel maneuvers, characterized by their inherent complexity and indeterminacy, requires vessel trajectory prediction system capable of modeling the multi-modality nature of future motion states. Conventional stochastic trajectory prediction methods utilize latent variables to represent the multi-modality of vessel motion, however, tends to overlook the complexity and dynamics inherent in maritime behavior. In contrast, we explicitly simulate the transition of vessel motion from uncertainty towards a state of certainty, effectively handling future indeterminacy in dynamic scenes. In this paper, we present a novel framework (DiffuTraj) to conceptualize the trajectory prediction task as a guided reverse process of motion pattern uncertainty diffusion, in which we progressively remove uncertainty from maritime regions to delineate the intended trajectory. Specifically, we encode the previous states of the target vessel, vessel-vessel interactions, and the environment context as guiding factors for trajectory generation. Subsequently, we devise a transformer-based conditional denoiser to capture spatio-temporal dependencies, enabling the generation of trajectories better aligned for particular maritime environment. Comprehensive experiments on vessel trajectory prediction benchmarks demonstrate the superiority of our method.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.

Trajectory generation has garnered significant attention from researchers in the field of spatio-temporal analysis, as it can generate substantial synthesized human mobility trajectories that enhance user privacy and alleviate data scarcity. However, existing trajectory generation methods often focus on improving trajectory generation quality from a singular perspective, lacking a comprehensive semantic understanding across various scales. Consequently, we are inspired to develop a HOlistic SEmantic Representation (HOSER) framework for navigational trajectory generation. Given an origin-and-destination (OD) pair and the starting time point of a latent trajectory, we first propose a Road Network Encoder to expand the receptive field of road- and zone-level semantics. Second, we design a Multi-Granularity Trajectory Encoder to integrate the spatio-temporal semantics of the generated trajectory at both the point and trajectory levels. Finally, we employ a Destination-Oriented Navigator to seamlessly integrate destination-oriented guidance. Extensive experiments on three real-world datasets demonstrate that HOSER outperforms state-of-the-art baselines by a significant margin. Moreover, the model's performance in few-shot learning and zero-shot learning scenarios further verifies the effectiveness of our holistic semantic representation.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory prediction datasets are generally imbalanced in favor of simpler samples and lack challenging scenarios. Such a long-tail effect causes prediction models to underperform on the tail portion of the data distribution containing safety-critical scenarios. Previous methods tackle the long-tail problem using methods such as contrastive learning and class-conditioned hypernetworks. These approaches, however, are not modular and cannot be applied to many machine learning architectures. In this work, we propose a modular model-agnostic framework for trajectory prediction that leverages a specialized mixture of experts. In our approach, each expert is trained with a specialized skill with respect to a particular part of the data. To produce predictions, we utilise a router network that selects the best expert by generating relative confidence scores. We conduct experimentation on common pedestrian trajectory prediction datasets and show that besides achieving state-of-the-art performance, our method significantly performs better on long-tail scenarios. We further conduct ablation studies to highlight the contribution of different proposed components.

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

We consider the problem of predicting the future trajectory of scene agents from egocentric views obtained from a moving platform. This problem is important in a variety of domains, particularly for autonomous systems making reactive or strategic decisions in navigation. In an attempt to address this problem, we introduce TITAN (Trajectory Inference using Targeted Action priors Network), a new model that incorporates prior positions, actions, and context to forecast future trajectory of agents and future ego-motion. In the absence of an appropriate dataset for this task, we created the TITAN dataset that consists of 700 labeled video-clips (with odometry) captured from a moving vehicle on highly interactive urban traffic scenes in Tokyo. Our dataset includes 50 labels including vehicle states and actions, pedestrian age groups, and targeted pedestrian action attributes that are organized hierarchically corresponding to atomic, simple/complex-contextual, transportive, and communicative actions. To evaluate our model, we conducted extensive experiments on the TITAN dataset, revealing significant performance improvement against baselines and state-of-the-art algorithms. We also report promising results from our Agent Importance Mechanism (AIM), a module which provides insight into assessment of perceived risk by calculating the relative influence of each agent on the future ego-trajectory. The dataset is available at https://usa.honda-ri.com/titan

Reliable multi-agent trajectory prediction is crucial for the safe planning and control of autonomous systems. Compared with single-agent cases, the major challenge in simultaneously processing multiple agents lies in modeling complex social interactions caused by various driving intentions and road conditions. Previous methods typically leverage graph-based message propagation or attention mechanism to encapsulate such interactions in the format of marginal probabilistic distributions. However, it is inherently sub-optimal. In this paper, we propose IPCC-TP, a novel relevance-aware module based on Incremental Pearson Correlation Coefficient to improve multi-agent interaction modeling. IPCC-TP learns pairwise joint Gaussian Distributions through the tightly-coupled estimation of the means and covariances according to interactive incremental movements. Our module can be conveniently embedded into existing multi-agent prediction methods to extend original motion distribution decoders. Extensive experiments on nuScenes and Argoverse 2 datasets demonstrate that IPCC-TP improves the performance of baselines by a large margin.

Autonomous Vehicles (AVs) collect and pseudo-label terabytes of multi-modal data localized to HD maps during normal fleet testing. However, identifying interesting and safety-critical scenarios from uncurated driving logs remains a significant challenge. Traditional scenario mining techniques are error-prone and prohibitively time-consuming, often relying on hand-crafted structured queries. In this work, we revisit spatio-temporal scenario mining through the lens of recent vision-language models (VLMs) to detect whether a described scenario occurs in a driving log and, if so, precisely localize it in both time and space. To address this problem, we introduce RefAV, a large-scale dataset of 10,000 diverse natural language queries that describe complex multi-agent interactions relevant to motion planning derived from 1000 driving logs in the Argoverse 2 Sensor dataset. We evaluate several referential multi-object trackers and present an empirical analysis of our baselines. Notably, we find that naively repurposing off-the-shelf VLMs yields poor performance, suggesting that scenario mining presents unique challenges. Our code and dataset are available at https://github.com/CainanD/RefAV/ and https://argoverse.github.io/user-guide/tasks/scenario_mining.html

This paper presents a Simple and effIcient Motion Prediction baseLine (SIMPL) for autonomous vehicles. Unlike conventional agent-centric methods with high accuracy but repetitive computations and scene-centric methods with compromised accuracy and generalizability, SIMPL delivers real-time, accurate motion predictions for all relevant traffic participants. To achieve improvements in both accuracy and inference speed, we propose a compact and efficient global feature fusion module that performs directed message passing in a symmetric manner, enabling the network to forecast future motion for all road users in a single feed-forward pass and mitigating accuracy loss caused by viewpoint shifting. Additionally, we investigate the continuous trajectory parameterization using Bernstein basis polynomials in trajectory decoding, allowing evaluations of states and their higher-order derivatives at any desired time point, which is valuable for downstream planning tasks. As a strong baseline, SIMPL exhibits highly competitive performance on Argoverse 1 & 2 motion forecasting benchmarks compared with other state-of-the-art methods. Furthermore, its lightweight design and low inference latency make SIMPL highly extensible and promising for real-world onboard deployment. We open-source the code at https://github.com/HKUST-Aerial-Robotics/SIMPL.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces M trajectory proposals corresponding to the M modes of the future trajectory distribution. The trajectory refinement network enhances each of the M proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

Generative models have shown great potential in trajectory planning. Recent studies demonstrate that anchor-guided generative models are effective in modeling the uncertainty of driving behaviors and improving overall performance. However, these methods rely on discrete anchor vocabularies that must sufficiently cover the trajectory distribution during testing to ensure robustness, inducing an inherent trade-off between vocabulary size and model performance. To overcome this limitation, we propose MeanFuser, an end-to-end autonomous driving method that enhances both efficiency and robustness through three key designs. (1) We introduce Gaussian Mixture Noise (GMN) to guide generative sampling, enabling a continuous representation of the trajectory space and eliminating the dependency on discrete anchor vocabularies. (2) We adapt ``MeanFlow Identity" to end-to-end planning, which models the mean velocity field between GMN and trajectory distribution instead of the instantaneous velocity field used in vanilla flow matching methods, effectively eliminating numerical errors from ODE solvers and significantly accelerating inference. (3) We design a lightweight Adaptive Reconstruction Module (ARM) that enables the model to implicitly select from all sampled proposals or reconstruct a new trajectory when none is satisfactory via attention weights.Experiments on the NAVSIM closed-loop benchmark demonstrate that MeanFuser achieves outstanding performance without the supervision of the PDM Score and exceptional inference efficiency, offering a robust and efficient solution for end-to-end autonomous driving. Our code and model are available at https://github.com/wjl2244/MeanFuser.

Trajectory data, capturing human actions and environmental states across various modalities, holds significant potential for enhancing AI agent capabilities, particularly in GUI environments. However, how to model the representation of trajectory-level data presents a significant challenge that has not been systematically addressed amid explosive trajectory data growth. In this work, we introduce Multimodal Trajectory Retrieval, bridging the gap between universal retrieval and agent-centric trajectory modeling. We construct the Unified Agent Trajectory Dataset (UATD) from annotated demonstrations and states across diverse real-world scenarios. Based on this, we present GAE-Bench, a benchmark containing a large number of trajectory-based retrieval pairs. In addition, we propose GAE-Retriever, a multimodal retrieval framework that adopts vision-language models and incorporates optimized contrastive learning through a token selection and the GradCache mechanism. Comprehensive evaluations across multiple datasets show that GAE-Retriever consistently outperforms strong baselines in retrieval recall, highlighting its effectiveness in advancing multimodal trajectory retrieval.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory .

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Recent research has made substantial progress on video reasoning, with many models leveraging spatio-temporal evidence chains to strengthen their inference capabilities. At the same time, a growing set of datasets and benchmarks now provides structured annotations designed to support and evaluate such reasoning. However, little attention has been paid to reasoning about how objects move between observations: no prior work has articulated the motion patterns by connecting successive observations, leaving trajectory understanding implicit and difficult to verify. We formalize this missing capability as Spatial-Temporal-Trajectory (STT) reasoning and introduce Motion-o, a motion-centric video understanding extension to visual language models that makes trajectories explicit and verifiable. To enable motion reasoning, we also introduce a trajectory-grounding dataset artifact that expands sparse keyframe supervision via augmentation to yield denser bounding box tracks and a stronger trajectory-level training signal. Finally, we introduce Motion Chain of Thought (MCoT), a structured reasoning pathway that makes object trajectories through discrete <motion/> tag summarizing per-object direction, speed, and scale (of velocity) change to explicitly connect grounded observations into trajectories. To train Motion-o, we design a reward function that compels the model to reason directly over visual evidence, all while requiring no architectural modifications. Empirical results demonstrate that Motion-o improves spatial-temporal grounding and trajectory prediction while remaining fully compatible with existing frameworks, establishing motion reasoning as a critical extension for evidence-based video understanding. Code is available at https://github.com/ostadabbas/Motion-o.

Human trajectory prediction is a practical task of predicting the future positions of pedestrians on the road, which typically covers all temporal ranges from short-term to long-term within a trajectory. However, existing works attempt to address the entire trajectory prediction with a singular, uniform training paradigm, neglecting the distinction between short-term and long-term dynamics in human trajectories. To overcome this limitation, we introduce a novel Progressive Pretext Task learning (PPT) framework, which progressively enhances the model's capacity of capturing short-term dynamics and long-term dependencies for the final entire trajectory prediction. Specifically, we elaborately design three stages of training tasks in the PPT framework. In the first stage, the model learns to comprehend the short-term dynamics through a stepwise next-position prediction task. In the second stage, the model is further enhanced to understand long-term dependencies through a destination prediction task. In the final stage, the model aims to address the entire future trajectory task by taking full advantage of the knowledge from previous stages. To alleviate the knowledge forgetting, we further apply a cross-task knowledge distillation. Additionally, we design a Transformer-based trajectory predictor, which is able to achieve highly efficient two-step reasoning by integrating a destination-driven prediction strategy and a group of learnable prompt embeddings. Extensive experiments on popular benchmarks have demonstrated that our proposed approach achieves state-of-the-art performance with high efficiency. Code is available at https://github.com/iSEE-Laboratory/PPT.

Trajectory prediction is fundamental in computer vision and autonomous driving, particularly for understanding pedestrian behavior and enabling proactive decision-making. Existing approaches in this field often assume precise and complete observational data, neglecting the challenges associated with out-of-view objects and the noise inherent in sensor data due to limited camera range, physical obstructions, and the absence of ground truth for denoised sensor data. Such oversights are critical safety concerns, as they can result in missing essential, non-visible objects. To bridge this gap, we present a novel method for out-of-sight trajectory prediction that leverages a vision-positioning technique. Our approach denoises noisy sensor observations in an unsupervised manner and precisely maps sensor-based trajectories of out-of-sight objects into visual trajectories. This method has demonstrated state-of-the-art performance in out-of-sight noisy sensor trajectory denoising and prediction on the Vi-Fi and JRDB datasets. By enhancing trajectory prediction accuracy and addressing the challenges of out-of-sight objects, our work significantly contributes to improving the safety and reliability of autonomous driving in complex environments. Our work represents the first initiative towards Out-Of-Sight Trajectory prediction (OOSTraj), setting a new benchmark for future research. The code is available at https://github.com/Hai-chao-Zhang/OOSTraj.

We present a novel framework for motion forecasting with Dual Consistency Constraints and Multi-Pseudo-Target supervision. The motion forecasting task predicts future trajectories of vehicles by incorporating spatial and temporal information from the past. A key design of DCMS is the proposed Dual Consistency Constraints that regularize the predicted trajectories under spatial and temporal perturbation during the training stage. In addition, we design a novel self-ensembling scheme to obtain accurate pseudo targets to model the multi-modality in motion forecasting through supervision with multiple targets explicitly, namely Multi-Pseudo-Target supervision. Our experimental results on the Argoverse motion forecasting benchmark show that DCMS significantly outperforms the state-of-the-art methods, achieving 1st place on the leaderboard. We also demonstrate that our proposed strategies can be incorporated into other motion forecasting approaches as general training schemes.

End-to-end multi-modal planning is a promising paradigm in autonomous driving, enabling decision-making with diverse trajectory candidates. A key component is a robust trajectory scorer capable of selecting the optimal trajectory from these candidates. While recent trajectory scorers focus on scoring either large sets of static trajectories or small sets of dynamically generated ones, both approaches face significant limitations in generalization. Static vocabularies provide effective coarse discretization but struggle to make fine-grained adaptation, while dynamic proposals offer detailed precision but fail to capture broader trajectory distributions. To overcome these challenges, we propose GTRS (Generalized Trajectory Scoring), a unified framework for end-to-end multi-modal planning that combines coarse and fine-grained trajectory evaluation. GTRS consists of three complementary innovations: (1) a diffusion-based trajectory generator that produces diverse fine-grained proposals; (2) a vocabulary generalization technique that trains a scorer on super-dense trajectory sets with dropout regularization, enabling its robust inference on smaller subsets; and (3) a sensor augmentation strategy that enhances out-of-domain generalization while incorporating refinement training for critical trajectory discrimination. As the winning solution of the Navsim v2 Challenge, GTRS demonstrates superior performance even with sub-optimal sensor inputs, approaching privileged methods that rely on ground-truth perception. Code will be available at https://github.com/NVlabs/GTRS.

This paper presents two variations of a novel stochastic prediction algorithm that enables mobile robots to accurately and robustly predict the future state of complex dynamic scenes. The proposed algorithm uses a variational autoencoder to predict a range of possible future states of the environment. The algorithm takes full advantage of the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects in the scene to improve prediction accuracy. Three simulated and real-world datasets collected by different robot models are used to demonstrate that the proposed algorithm is able to achieve more accurate and robust prediction performance than other prediction algorithms. Furthermore, a predictive uncertainty-aware planner is proposed to demonstrate the effectiveness of the proposed predictor in simulation and real-world navigation experiments. Implementations are open source at https://github.com/TempleRAIL/SOGMP.

This article presents a family of Stochastic Cartographic Occupancy Prediction Engines (SCOPEs) that enable mobile robots to predict the future states of complex dynamic environments. They do this by accounting for the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects in the scene, and they generate a range of possible future states of the environment. These prediction engines are software-optimized for real-time performance for navigation in crowded dynamic scenes, achieving up to 89 times faster inference speed and 8 times less memory usage than other state-of-the-art engines. Three simulated and real-world datasets collected by different robot models are used to demonstrate that these proposed prediction algorithms are able to achieve more accurate and robust stochastic prediction performance than other algorithms. Furthermore, a series of simulation and hardware navigation experiments demonstrate that the proposed predictive uncertainty-aware navigation framework with these stochastic prediction engines is able to improve the safe navigation performance of current state-of-the-art model- and learning-based control policies.

We present a multi-modal trajectory generation and selection algorithm for real-world mapless outdoor navigation in human-centered environments. Such environments contain rich features like crosswalks, grass, and curbs, which are easily interpretable by humans, but not by mobile robots. We aim to compute suitable trajectories that (1) satisfy the environment-specific traversability constraints and (2) generate human-like paths while navigating on crosswalks, sidewalks, etc. Our formulation uses a Conditional Variational Autoencoder (CVAE) generative model enhanced with traversability constraints to generate multiple candidate trajectories for global navigation. We develop a visual prompting approach and leverage the Visual Language Model's (VLM) zero-shot ability of semantic understanding and logical reasoning to choose the best trajectory given the contextual information about the task. We evaluate our method in various outdoor scenes with wheeled robots and compare the performance with other global navigation algorithms. In practice, we observe an average improvement of 20.81% in satisfying traversability constraints and 28.51% in terms of human-like navigation in four different outdoor navigation scenarios.

In this paper, we propose ProTracker, a novel framework for robust and accurate long-term dense tracking of arbitrary points in videos. The key idea of our method is incorporating probabilistic integration to refine multiple predictions from both optical flow and semantic features for robust short-term and long-term tracking. Specifically, we integrate optical flow estimations in a probabilistic manner, producing smooth and accurate trajectories by maximizing the likelihood of each prediction. To effectively re-localize challenging points that disappear and reappear due to occlusion, we further incorporate long-term feature correspondence into our flow predictions for continuous trajectory generation. Extensive experiments show that ProTracker achieves the state-of-the-art performance among unsupervised and self-supervised approaches, and even outperforms supervised methods on several benchmarks. Our code and model will be publicly available upon publication.

In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic environments. Our model enhances the accuracy and reliability of trajectory predictions by incorporating uncertainty estimation and complex agent interactions. Through extensive experimentation on public datasets such as NGSIM, HighD, and MoCAD, our model significantly outperforms existing state-of-the-art methods. We demonstrate its ability to capture the underlying spatial-temporal dynamics of traffic scenarios and improve prediction precision, especially in complex environments. The proposed model showcases strong potential for application in real-world autonomous driving systems.

The emergence of multi-modal foundation models has markedly transformed the technology for autonomous driving, shifting away from conventional and mostly hand-crafted design choices towards unified, foundation-model-based approaches, capable of directly inferring motion trajectories from raw sensory inputs. This new class of methods can also incorporate natural language as an additional modality, with Vision-Language-Action (VLA) models serving as a representative example. In this review, we provide a comprehensive examination of such methods through a unifying taxonomy to critically evaluate their architectural design choices, methodological strengths, and their inherent capabilities and limitations. Our survey covers 37 recently proposed approaches that span the landscape of trajectory planning with foundation models. Furthermore, we assess these approaches with respect to the openness of their source code and datasets, offering valuable information to practitioners and researchers. We provide an accompanying webpage that catalogues the methods based on our taxonomy, available at: https://github.com/fiveai/FMs-for-driving-trajectories

Vehicle trajectory prediction has increasingly relied on data-driven solutions, but their ability to scale to different data domains and the impact of larger dataset sizes on their generalization remain under-explored. While these questions can be studied by employing multiple datasets, it is challenging due to several discrepancies, e.g., in data formats, map resolution, and semantic annotation types. To address these challenges, we introduce UniTraj, a comprehensive framework that unifies various datasets, models, and evaluation criteria, presenting new opportunities for the vehicle trajectory prediction field. In particular, using UniTraj, we conduct extensive experiments and find that model performance significantly drops when transferred to other datasets. However, enlarging data size and diversity can substantially improve performance, leading to a new state-of-the-art result for the nuScenes dataset. We provide insights into dataset characteristics to explain these findings. The code can be found here: https://github.com/vita-epfl/UniTraj

Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex distributions, yet can be trained efficiently using exact maximum likelihood, unlike GANs or VAEs. Our proposed model is autoregressive and uses LSTMs to enable arbitrarily long time-dependencies. Importantly, is is also causal, meaning that each pose in the output sequence is generated without access to poses or control inputs from future time steps; this absence of algorithmic latency is important for interactive applications with real-time motion control. The approach can in principle be applied to any type of motion since it does not make restrictive, task-specific assumptions regarding the motion or the character morphology. We evaluate the models on motion-capture datasets of human and quadruped locomotion. Objective and subjective results show that randomly-sampled motion from the proposed method outperforms task-agnostic baselines and attains a motion quality close to recorded motion capture.

The capability to efficiently search for objects in complex environments is fundamental for many real-world robot applications. Recent advances in open-vocabulary vision models have resulted in semantically-informed object navigation methods that allow a robot to search for an arbitrary object without prior training. However, these zero-shot methods have so far treated the environment as unknown for each consecutive query. In this paper we introduce a new benchmark for zero-shot multi-object navigation, allowing the robot to leverage information gathered from previous searches to more efficiently find new objects. To address this problem we build a reusable open-vocabulary feature map tailored for real-time object search. We further propose a probabilistic-semantic map update that mitigates common sources of errors in semantic feature extraction and leverage this semantic uncertainty for informed multi-object exploration. We evaluate our method on a set of object navigation tasks in both simulation as well as with a real robot, running in real-time on a Jetson Orin AGX. We demonstrate that it outperforms existing state-of-the-art approaches both on single and multi-object navigation tasks. Additional videos, code and the multi-object navigation benchmark will be available on https://finnbsch.github.io/OneMap.

Without manually annotated identities, unsupervised multi-object trackers are inferior to learning reliable feature embeddings. It causes the similarity-based inter-frame association stage also be error-prone, where an uncertainty problem arises. The frame-by-frame accumulated uncertainty prevents trackers from learning the consistent feature embedding against time variation. To avoid this uncertainty problem, recent self-supervised techniques are adopted, whereas they failed to capture temporal relations. The interframe uncertainty still exists. In fact, this paper argues that though the uncertainty problem is inevitable, it is possible to leverage the uncertainty itself to improve the learned consistency in turn. Specifically, an uncertainty-based metric is developed to verify and rectify the risky associations. The resulting accurate pseudo-tracklets boost learning the feature consistency. And accurate tracklets can incorporate temporal information into spatial transformation. This paper proposes a tracklet-guided augmentation strategy to simulate tracklets' motion, which adopts a hierarchical uncertainty-based sampling mechanism for hard sample mining. The ultimate unsupervised MOT framework, namely U2MOT, is proven effective on MOT-Challenges and VisDrone-MOT benchmark. U2MOT achieves a SOTA performance among the published supervised and unsupervised trackers.

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of multiple interacting agents. Only focusing on marginal metrics can lead to unnatural predictions, such as colliding trajectories or diverging trajectories for people who are clearly walking together as a group. Consequently, methods optimized for marginal metrics lead to overly-optimistic estimations of performance, which is detrimental to progress in trajectory forecasting research. In response to the limitations of marginal metrics, we present the first comprehensive evaluation of state-of-the-art (SOTA) trajectory forecasting methods with respect to multi-agent metrics (joint metrics): JADE, JFDE, and collision rate. We demonstrate the importance of joint metrics as opposed to marginal metrics with quantitative evidence and qualitative examples drawn from the ETH / UCY and Stanford Drone datasets. We introduce a new loss function incorporating joint metrics that, when applied to a SOTA trajectory forecasting method, achieves a 7% improvement in JADE / JFDE on the ETH / UCY datasets with respect to the previous SOTA. Our results also indicate that optimizing for joint metrics naturally leads to an improvement in interaction modeling, as evidenced by a 16% decrease in mean collision rate on the ETH / UCY datasets with respect to the previous SOTA.

Predicting future trajectories of surrounding agents is essential for safety-critical autonomous driving. Most existing work focuses on predicting marginal trajectories for each agent independently. However, it has rarely been explored in predicting joint trajectories for interactive agents. In this work, we propose Bi-level Future Fusion (BiFF) to explicitly capture future interactions between interactive agents. Concretely, BiFF fuses the high-level future intentions followed by low-level future behaviors. Then the polyline-based coordinate is specifically designed for multi-agent prediction to ensure data efficiency, frame robustness, and prediction accuracy. Experiments show that BiFF achieves state-of-the-art performance on the interactive prediction benchmark of Waymo Open Motion Dataset.

End-to-end autonomous driving unifies tasks in a differentiable framework, enabling planning-oriented optimization and attracting growing attention. Current methods aggregate historical information either through dense historical bird's-eye-view (BEV) features or by querying a sparse memory bank, following paradigms inherited from detection. However, we argue that these paradigms either omit historical information in motion planning or fail to align with its multi-step nature, which requires predicting or planning multiple future time steps. In line with the philosophy of future is a continuation of past, we propose BridgeAD, which reformulates motion and planning queries as multi-step queries to differentiate the queries for each future time step. This design enables the effective use of historical prediction and planning by applying them to the appropriate parts of the end-to-end system based on the time steps, which improves both perception and motion planning. Specifically, historical queries for the current frame are combined with perception, while queries for future frames are integrated with motion planning. In this way, we bridge the gap between past and future by aggregating historical insights at every time step, enhancing the overall coherence and accuracy of the end-to-end autonomous driving pipeline. Extensive experiments on the nuScenes dataset in both open-loop and closed-loop settings demonstrate that BridgeAD achieves state-of-the-art performance.

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

Tracking by detection has been the prevailing paradigm in the field of Multi-object Tracking (MOT). These methods typically rely on the Kalman Filter to estimate the future locations of objects, assuming linear object motion. However, they fall short when tracking objects exhibiting nonlinear and diverse motion in scenarios like dancing and sports. In addition, there has been limited focus on utilizing learning-based motion predictors in MOT. To address these challenges, we resort to exploring data-driven motion prediction methods. Inspired by the great expectation of state space models (SSMs), such as Mamba, in long-term sequence modeling with near-linear complexity, we introduce a Mamba-based motion model named Mamba moTion Predictor (MTP). MTP is designed to model the complex motion patterns of objects like dancers and athletes. Specifically, MTP takes the spatial-temporal location dynamics of objects as input, captures the motion pattern using a bi-Mamba encoding layer, and predicts the next motion. In real-world scenarios, objects may be missed due to occlusion or motion blur, leading to premature termination of their trajectories. To tackle this challenge, we further expand the application of MTP. We employ it in an autoregressive way to compensate for missing observations by utilizing its own predictions as inputs, thereby contributing to more consistent trajectories. Our proposed tracker, MambaTrack, demonstrates advanced performance on benchmarks such as Dancetrack and SportsMOT, which are characterized by complex motion and severe occlusion.

Predicting the trajectories of road agents is essential for autonomous driving systems. The recent mainstream methods follow a static paradigm, which predicts the future trajectory by using a fixed duration of historical frames. These methods make the predictions independently even at adjacent time steps, which leads to potential instability and temporal inconsistency. As successive time steps have largely overlapping historical frames, their forecasting should have intrinsic correlation, such as overlapping predicted trajectories should be consistent, or be different but share the same motion goal depending on the road situation. Motivated by this, in this work, we introduce HPNet, a novel dynamic trajectory forecasting method. Aiming for stable and accurate trajectory forecasting, our method leverages not only historical frames including maps and agent states, but also historical predictions. Specifically, we newly design a Historical Prediction Attention module to automatically encode the dynamic relationship between successive predictions. Besides, it also extends the attention range beyond the currently visible window benefitting from the use of historical predictions. The proposed Historical Prediction Attention together with the Agent Attention and Mode Attention is further formulated as the Triple Factorized Attention module, serving as the core design of HPNet.Experiments on the Argoverse and INTERACTION datasets show that HPNet achieves state-of-the-art performance, and generates accurate and stable future trajectories. Our code are available at https://github.com/XiaolongTang23/HPNet.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds--the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n^{-1/d+ρ}), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.

Most existing mobile robotic datasets primarily capture static scenes, limiting their utility for evaluating robotic performance in dynamic environments. To address this, we present a mobile robot oriented large-scale indoor dataset, denoted as THUD++ (TsingHua University Dynamic) robotic dataset, for dynamic scene understanding. Our current dataset includes 13 large-scale dynamic scenarios, combining both real-world and synthetic data collected with a real robot platform and a physical simulation platform, respectively. The RGB-D dataset comprises over 90K image frames, 20M 2D/3D bounding boxes of static and dynamic objects, camera poses, and IMU. The trajectory dataset covers over 6,000 pedestrian trajectories in indoor scenes. Additionally, the dataset is augmented with a Unity3D-based simulation platform, allowing researchers to create custom scenes and test algorithms in a controlled environment. We evaluate state-of-the-art methods on THUD++ across mainstream indoor scene understanding tasks, e.g., 3D object detection, semantic segmentation, relocalization, pedestrian trajectory prediction, and navigation. Our experiments highlight the challenges mobile robots encounter in indoor environments, especially when navigating in complex, crowded, and dynamic scenes. By sharing this dataset, we aim to accelerate the development and testing of mobile robot algorithms, contributing to real-world robotic applications.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire time-series trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Code is publicly available at https://github.com/inhwanbae/LMTrajectory .

In robot manipulation, robot learning has become a prevailing approach. However, generative models within this field face a fundamental trade-off between the slow, iterative sampling of diffusion models and the architectural constraints of faster Flow-based methods, which often rely on explicit consistency losses. To address these limitations, we introduce MP1, which pairs 3D point-cloud inputs with the MeanFlow paradigm to generate action trajectories in one network function evaluation (1-NFE). By directly learning the interval-averaged velocity via the "MeanFlow Identity", our policy avoids any additional consistency constraints. This formulation eliminates numerical ODE-solver errors during inference, yielding more precise trajectories. MP1 further incorporates CFG for improved trajectory controllability while retaining 1-NFE inference without reintroducing structural constraints. Because subtle scene-context variations are critical for robot learning, especially in few-shot learning, we introduce a lightweight Dispersive Loss that repels state embeddings during training, boosting generalization without slowing inference. We validate our method on the Adroit and Meta-World benchmarks, as well as in real-world scenarios. Experimental results show MP1 achieves superior average task success rates, outperforming DP3 by 10.2% and FlowPolicy by 7.3%. Its average inference time is only 6.8 ms-19x faster than DP3 and nearly 2x faster than FlowPolicy. Our code is available at https://github.com/LogSSim/MP1.git.

Combining motion prediction and motion planning offers a promising framework for enhancing interactions between automated vehicles and other traffic participants. However, this introduces challenges in conditioning predictions on navigation goals and ensuring stable, kinematically feasible trajectories. Addressing the former challenge, this paper investigates the extension of attention-based motion prediction models with navigation information. By integrating the ego vehicle's intended route and goal pose into the model architecture, we bridge the gap between multi-agent motion prediction and goal-based motion planning. We propose and evaluate several architectural navigation integration strategies to our model on the nuPlan dataset. Our results demonstrate the potential of prediction-driven motion planning, highlighting how navigation information can enhance both prediction and planning tasks. Our implementation is at: https://github.com/KIT-MRT/future-motion.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

Multiple object tracking in complex scenarios - such as coordinated dance performances, team sports, or dynamic animal groups - presents unique challenges. In these settings, objects frequently move in coordinated patterns, occlude each other, and exhibit long-term dependencies in their trajectories. However, it remains a key open research question on how to model long-range dependencies within tracklets, interdependencies among tracklets, and the associated temporal occlusions. To this end, we introduce Samba, a novel linear-time set-of-sequences model designed to jointly process multiple tracklets by synchronizing the multiple selective state-spaces used to model each tracklet. Samba autoregressively predicts the future track query for each sequence while maintaining synchronized long-term memory representations across tracklets. By integrating Samba into a tracking-by-propagation framework, we propose SambaMOTR, the first tracker effectively addressing the aforementioned issues, including long-range dependencies, tracklet interdependencies, and temporal occlusions. Additionally, we introduce an effective technique for dealing with uncertain observations (MaskObs) and an efficient training recipe to scale SambaMOTR to longer sequences. By modeling long-range dependencies and interactions among tracked objects, SambaMOTR implicitly learns to track objects accurately through occlusions without any hand-crafted heuristics. Our approach significantly surpasses prior state-of-the-art on the DanceTrack, BFT, and SportsMOT datasets.

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic

Motion behaviour is driven by several factors -- goals, presence and actions of neighbouring agents, social relations, physical and social norms, the environment with its variable characteristics, and further. Most factors are not directly observable and must be modelled from context. Trajectory prediction, is thus a hard problem, and has seen increasing attention from researchers in the recent years. Prediction of motion, in application, must be realistic, diverse and controllable. In spite of increasing focus on multimodal trajectory generation, most methods still lack means for explicitly controlling different modes of the data generation. Further, most endeavours invest heavily in designing special mechanisms to learn the interactions in latent space. We present Conditional Speed GAN (CSG), that allows controlled generation of diverse and socially acceptable trajectories, based on user controlled speed. During prediction, CSG forecasts future speed from latent space and conditions its generation based on it. CSG is comparable to state-of-the-art GAN methods in terms of the benchmark distance metrics, while being simple and useful for simulation and data augmentation for different contexts such as fast or slow paced environments. Additionally, we compare the effect of different aggregation mechanisms and show that a naive approach of concatenation works comparable to its attention and pooling alternatives.

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Despite real-time planners exhibiting remarkable performance in autonomous driving, the growing exploration of Large Language Models (LLMs) has opened avenues for enhancing the interpretability and controllability of motion planning. Nevertheless, LLM-based planners continue to encounter significant challenges, including elevated resource consumption and extended inference times, which pose substantial obstacles to practical deployment. In light of these challenges, we introduce AsyncDriver, a new asynchronous LLM-enhanced closed-loop framework designed to leverage scene-associated instruction features produced by LLM to guide real-time planners in making precise and controllable trajectory predictions. On one hand, our method highlights the prowess of LLMs in comprehending and reasoning with vectorized scene data and a series of routing instructions, demonstrating its effective assistance to real-time planners. On the other hand, the proposed framework decouples the inference processes of the LLM and real-time planners. By capitalizing on the asynchronous nature of their inference frequencies, our approach have successfully reduced the computational cost introduced by LLM, while maintaining comparable performance. Experiments show that our approach achieves superior closed-loop evaluation performance on nuPlan's challenging scenarios.

Motion forecasting for autonomous driving is a challenging task because complex driving scenarios result in a heterogeneous mix of static and dynamic inputs. It is an open problem how best to represent and fuse information about road geometry, lane connectivity, time-varying traffic light state, and history of a dynamic set of agents and their interactions into an effective encoding. To model this diverse set of input features, many approaches proposed to design an equally complex system with a diverse set of modality specific modules. This results in systems that are difficult to scale, extend, or tune in rigorous ways to trade off quality and efficiency. In this paper, we present Wayformer, a family of attention based architectures for motion forecasting that are simple and homogeneous. Wayformer offers a compact model description consisting of an attention based scene encoder and a decoder. In the scene encoder we study the choice of early, late and hierarchical fusion of the input modalities. For each fusion type we explore strategies to tradeoff efficiency and quality via factorized attention or latent query attention. We show that early fusion, despite its simplicity of construction, is not only modality agnostic but also achieves state-of-the-art results on both Waymo Open MotionDataset (WOMD) and Argoverse leaderboards, demonstrating the effectiveness of our design philosophy

We present TartanGround, a large-scale, multi-modal dataset to advance the perception and autonomy of ground robots operating in diverse environments. This dataset, collected in various photorealistic simulation environments includes multiple RGB stereo cameras for 360-degree coverage, along with depth, optical flow, stereo disparity, LiDAR point clouds, ground truth poses, semantic segmented images, and occupancy maps with semantic labels. Data is collected using an integrated automatic pipeline, which generates trajectories mimicking the motion patterns of various ground robot platforms, including wheeled and legged robots. We collect 910 trajectories across 70 environments, resulting in 1.5 million samples. Evaluations on occupancy prediction and SLAM tasks reveal that state-of-the-art methods trained on existing datasets struggle to generalize across diverse scenes. TartanGround can serve as a testbed for training and evaluation of a broad range of learning-based tasks, including occupancy prediction, SLAM, neural scene representation, perception-based navigation, and more, enabling advancements in robotic perception and autonomy towards achieving robust models generalizable to more diverse scenarios. The dataset and codebase are available on the webpage: https://tartanair.org/tartanground

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

Recent temporal LiDAR-based 3D object detectors achieve promising performance based on the two-stage proposal-based approach. They generate 3D box candidates from the first-stage dense detector, followed by different temporal aggregation methods. However, these approaches require per-frame objects or whole point clouds, posing challenges related to memory bank utilization. Moreover, point clouds and trajectory features are combined solely based on concatenation, which may neglect effective interactions between them. In this paper, we propose a point-trajectory transformer with long short-term memory for efficient temporal 3D object detection. To this end, we only utilize point clouds of current-frame objects and their historical trajectories as input to minimize the memory bank storage requirement. Furthermore, we introduce modules to encode trajectory features, focusing on long short-term and future-aware perspectives, and then effectively aggregate them with point cloud features. We conduct extensive experiments on the large-scale Waymo dataset to demonstrate that our approach performs well against state-of-the-art methods. Code and models will be made publicly available at https://github.com/kuanchihhuang/PTT.

A longstanding challenge for self-driving development is simulating dynamic driving scenarios seeded from recorded driving logs. In pursuit of this functionality, we apply tools from discrete sequence modeling to model how vehicles, pedestrians and cyclists interact in driving scenarios. Using a simple data-driven tokenization scheme, we discretize trajectories to centimeter-level resolution using a small vocabulary. We then model the multi-agent sequence of motion tokens with a GPT-like encoder-decoder that is autoregressive in time and takes into account intra-timestep interaction between agents. Scenarios sampled from our model exhibit state-of-the-art realism; our model tops the Waymo Sim Agents Benchmark, surpassing prior work along the realism meta metric by 3.3% and along the interaction metric by 9.9%. We ablate our modeling choices in full autonomy and partial autonomy settings, and show that the representations learned by our model can quickly be adapted to improve performance on nuScenes. We additionally evaluate the scalability of our model with respect to parameter count and dataset size, and use density estimates from our model to quantify the saliency of context length and intra-timestep interaction for the traffic modeling task.

Recent advances in motion planning for autonomous driving have led to models capable of generating high-quality trajectories. However, most existing planners tend to fix their policy after supervised training, leading to consistent but rigid driving behaviors. This limits their ability to reflect human preferences or adapt to dynamic, instruction-driven demands. In this work, we propose a diffusion-based multi-head trajectory planner(M-diffusion planner). During the early training stage, all output heads share weights to learn to generate high-quality trajectories. Leveraging the probabilistic nature of diffusion models, we then apply Group Relative Policy Optimization (GRPO) to fine-tune the pre-trained model for diverse policy-specific behaviors. At inference time, we incorporate a large language model (LLM) to guide strategy selection, enabling dynamic, instruction-aware planning without switching models. Closed-loop simulation demonstrates that our post-trained planner retains strong planning capability while achieving state-of-the-art (SOTA) performance on the nuPlan val14 benchmark. Open-loop results further show that the generated trajectories exhibit clear diversity, effectively satisfying multi-modal driving behavior requirements. The code and related experiments will be released upon acceptance of the paper.

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim to tackle the challenge of learning general trajectory forecasting representations under limited data availability. We propose a pipeline-level solution to mitigate the issue of data scarcity in trajectory forecasting. The solution is composed of two parts: firstly, we adopt HD map augmentation and trajectory synthesis for generating driving data, and then we learn representations by pre-training on them. Specifically, we apply vector transformations to reshape the maps, and then employ a rule-based model to generate trajectories on both original and augmented scenes; thus enlarging the driving data without collecting additional real ones. To foster the learning of general representations within this augmented dataset, we comprehensively explore the different pre-training strategies, including extending the concept of a Masked AutoEncoder (MAE) for trajectory forecasting. Without bells and whistles, our proposed pipeline-level solution is general, simple, yet effective: we conduct extensive experiments to demonstrate the effectiveness of our data expansion and pre-training strategies, which outperform the baseline prediction model by large margins, e.g. 5.04%, 3.84% and 8.30% in terms of MR_6, minADE_6 and minFDE_6. The pre-training dataset and the codes for pre-training and fine-tuning are released at https://github.com/yhli123/Pretraining_on_Synthetic_Driving_Data_for_Trajectory_Prediction.

Simulating realistic behaviors of traffic agents is pivotal for efficiently validating the safety of autonomous driving systems. Existing data-driven simulators primarily use an encoder-decoder architecture to encode the historical trajectories before decoding the future. However, the heterogeneity between encoders and decoders complicates the models, and the manual separation of historical and future trajectories leads to low data utilization. Given these limitations, we propose BehaviorGPT, a homogeneous and fully autoregressive Transformer designed to simulate the sequential behavior of multiple agents. Crucially, our approach discards the traditional separation between "history" and "future" by modeling each time step as the "current" one for motion generation, leading to a simpler, more parameter- and data-efficient agent simulator. We further introduce the Next-Patch Prediction Paradigm (NP3) to mitigate the negative effects of autoregressive modeling, in which models are trained to reason at the patch level of trajectories and capture long-range spatial-temporal interactions. Despite having merely 3M model parameters, BehaviorGPT won first place in the 2024 Waymo Open Sim Agents Challenge with a realism score of 0.7473 and a minADE score of 1.4147, demonstrating its exceptional performance in traffic agent simulation.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

We introduce Masked Trajectory Models (MTM) as a generic abstraction for sequential decision making. MTM takes a trajectory, such as a state-action sequence, and aims to reconstruct the trajectory conditioned on random subsets of the same trajectory. By training with a highly randomized masking pattern, MTM learns versatile networks that can take on different roles or capabilities, by simply choosing appropriate masks at inference time. For example, the same MTM network can be used as a forward dynamics model, inverse dynamics model, or even an offline RL agent. Through extensive experiments in several continuous control tasks, we show that the same MTM network -- i.e. same weights -- can match or outperform specialized networks trained for the aforementioned capabilities. Additionally, we find that state representations learned by MTM can significantly accelerate the learning speed of traditional RL algorithms. Finally, in offline RL benchmarks, we find that MTM is competitive with specialized offline RL algorithms, despite MTM being a generic self-supervised learning method without any explicit RL components. Code is available at https://github.com/facebookresearch/mtm

Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs.

Next Location Prediction is a fundamental task in the study of human mobility, with wide-ranging applications in transportation planning, urban governance, and epidemic forecasting. In practice, when humans attempt to predict the next location in a trajectory, they often visualize the trajectory on a map and reason based on road connectivity and movement trends. However, the vast majority of existing next-location prediction models do not reason over maps in the way that humans do. Fortunately, the recent development of Vision-Language Models (VLMs) has demonstrated strong capabilities in visual perception and even visual reasoning. This opens up a new possibility: by rendering both the road network and trajectory onto an image and leveraging the reasoning abilities of VLMs, we can enable models to perform trajectory inference in a human-like manner. To explore this idea, we first propose a method called Vision-Guided Location Search (VGLS), which evaluates whether a general-purpose VLM is capable of trajectory-based reasoning without modifying any of its internal parameters. Based on insights from the VGLS results, we further propose our main approach: VLMLocPredictor, which is composed of two stages: In the first stage, we design two Supervised Fine-Tuning (SFT) tasks that help the VLM understand road network and trajectory structures and acquire basic reasoning ability on such visual inputs. In the second stage, we introduce Reinforcement Learning from Visual Map Feedback, enabling the model to self-improve its next-location prediction ability through interaction with the environment. Experiments conducted on datasets from four different cities show that our method achieves state-of-the-art (SOTA) performance and exhibits superior cross-city generalization compared to other LLM-based approaches.

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Temporal motion modeling has always been a key component in multiple object tracking (MOT) which can ensure smooth trajectory movement and provide accurate positional information to enhance association precision. However, current motion models struggle to be both efficient and effective across different application scenarios. To this end, we propose TrackSSM inspired by the recently popular state space models (SSM), a unified encoder-decoder motion framework that uses data-dependent state space model to perform temporal motion of trajectories. Specifically, we propose Flow-SSM, a module that utilizes the position and motion information from historical trajectories to guide the temporal state transition of object bounding boxes. Based on Flow-SSM, we design a flow decoder. It is composed of a cascaded motion decoding module employing Flow-SSM, which can use the encoded flow information to complete the temporal position prediction of trajectories. Additionally, we propose a Step-by-Step Linear (S^2L) training strategy. By performing linear interpolation between the positions of the object in the previous frame and the current frame, we construct the pseudo labels of step-by-step linear training, ensuring that the trajectory flow information can better guide the object bounding box in completing temporal transitions. TrackSSM utilizes a simple Mamba-Block to build a motion encoder for historical trajectories, forming a temporal motion model with an encoder-decoder structure in conjunction with the flow decoder. TrackSSM is applicable to various tracking scenarios and achieves excellent tracking performance across multiple benchmarks, further extending the potential of SSM-like temporal motion models in multi-object tracking tasks. Code and models are publicly available at https://github.com/Xavier-Lin/TrackSSM.

Tracking a point through a video can be a challenging task due to uncertainty arising from visual obfuscations, such as appearance changes and occlusions. Although current state-of-the-art discriminative models excel in regressing long-term point trajectory estimates -- even through occlusions -- they are limited to regressing to a mean (or mode) in the presence of uncertainty, and fail to capture multi-modality. To overcome this limitation, we introduce Generative Point Tracker (GenPT), a generative framework for modelling multi-modal trajectories. GenPT is trained with a novel flow matching formulation that combines the iterative refinement of discriminative trackers, a window-dependent prior for cross-window consistency, and a variance schedule tuned specifically for point coordinates. We show how our model's generative capabilities can be leveraged to improve point trajectory estimates by utilizing a best-first search strategy on generated samples during inference, guided by the model's own confidence of its predictions. Empirically, we evaluate GenPT against the current state of the art on the standard PointOdyssey, Dynamic Replica, and TAP-Vid benchmarks. Further, we introduce a TAP-Vid variant with additional occlusions to assess occluded point tracking performance and highlight our model's ability to capture multi-modality. GenPT is capable of capturing the multi-modality in point trajectories, which translates to state-of-the-art tracking accuracy on occluded points, while maintaining competitive tracking accuracy on visible points compared to extant discriminative point trackers.

Forecasting future trajectories of agents in complex traffic scenes requires reliable and efficient predictions for all agents in the scene. However, existing methods for trajectory prediction are either inefficient or sacrifice accuracy. To address this challenge, we propose ADAPT, a novel approach for jointly predicting the trajectories of all agents in the scene with dynamic weight learning. Our approach outperforms state-of-the-art methods in both single-agent and multi-agent settings on the Argoverse and Interaction datasets, with a fraction of their computational overhead. We attribute the improvement in our performance: first, to the adaptive head augmenting the model capacity without increasing the model size; second, to our design choices in the endpoint-conditioned prediction, reinforced by gradient stopping. Our analyses show that ADAPT can focus on each agent with adaptive prediction, allowing for accurate predictions efficiently. https://KUIS-AI.github.io/adapt

Recent success in large multimodal models (LMMs) has sparked promising applications of agents capable of autonomously completing complex web tasks. While open-source LMM agents have made significant advances in offline evaluation benchmarks, their performance still falls substantially short of human-level capabilities in more realistic online settings. A key bottleneck is the lack of diverse and large-scale trajectory-level datasets across various domains, which are expensive to collect. In this paper, we address this challenge by developing a scalable recipe to synthesize the largest and most diverse trajectory-level dataset to date, containing over 94K successful multimodal web trajectories, spanning 49K unique URLs, 720K screenshots, and 33M web elements. In particular, we leverage extensive web exploration and refinement to obtain diverse task intents. The average cost is 28 cents per successful trajectory, making it affordable to a wide range of users in the community. Leveraging this dataset, we train Explorer, a multimodal web agent, and demonstrate strong performance on both offline and online web agent benchmarks such as Mind2Web-Live, Multimodal-Mind2Web, and MiniWob++. Additionally, our experiments highlight data scaling as a key driver for improving web agent capabilities. We hope this study makes state-of-the-art LMM-based agent research at a larger scale more accessible.

End-to-end multi-modal planning has been widely adopted to model the uncertainty of driving behavior, typically by scoring candidate trajectories and selecting the optimal one. Existing approaches generally fall into two categories: scoring a large static trajectory vocabulary, or scoring a small set of dynamically generated proposals. While static vocabularies often suffer from coarse discretization of the action space, dynamic proposals provide finer-grained precision and have shown stronger empirical performance on existing benchmarks. However, it remains unclear whether dynamic generation is fundamentally necessary, or whether static vocabularies can already achieve comparable performance when they are sufficiently dense to cover the action space. In this work, we start with a systematic scaling study of Hydra-MDP, a representative scoring-based method, revealing that performance consistently improves as trajectory anchors become denser, without exhibiting saturation before computational constraints are reached. Motivated by this observation, we propose SparseDriveV2 to push the performance boundary of scoring-based planning through two complementary innovations: (1) a scalable vocabulary representation with a factorized structure that decomposes trajectories into geometric paths and velocity profiles, enabling combinatorial coverage of the action space, and (2) a scalable scoring strategy with coarse factorized scoring over paths and velocity profiles followed by fine-grained scoring on a small set of composed trajectories. By combining these two techniques, SparseDriveV2 achieves 92.0 PDMS and 90.1 EPDMS on NAVSIM, with 89.15 Driving Score and 70.00 Success Rate on Bench2Drive with a lightweight ResNet-34 as backbone. Code and model are released at https://github.com/swc-17/SparseDriveV2.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

Video anomaly detection deals with the recognition of abnormal events in videos. Apart from the visual signal, video anomaly detection has also been addressed with the use of skeleton sequences. We propose a holistic representation of skeleton trajectories to learn expected motions across segments at different times. Our approach uses multitask learning to reconstruct any continuous unobserved temporal segment of the trajectory allowing the extrapolation of past or future segments and the interpolation of in-between segments. We use an end-to-end attention-based encoder-decoder. We encode temporally occluded trajectories, jointly learn latent representations of the occluded segments, and reconstruct trajectories based on expected motions across different temporal segments. Extensive experiments on three trajectory-based video anomaly detection datasets show the advantages and effectiveness of our approach with state-of-the-art results on anomaly detection in skeleton trajectories.

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the long tail of possible events, which are rarely observed in limited datasets. On the other hand, planning for worst-case motions leads to overtly conservative behavior and a "frozen robot". Instead, we aim to learn forecasts that predict counterfactuals that humans guard against. We propose a novel game-theoretic framework for joint planning and forecasting with the payoff being the performance of the planner against the demonstrator, and present practical algorithms to train models in an end-to-end fashion. We demonstrate that our proposed algorithm results in safer plans in a crowd navigation simulator and real-world datasets of pedestrian motion. We release our code at https://github.com/portal-cornell/Game-Theoretic-Forecasting-Planning.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Large-scale datasets have fueled recent advancements in AI-based autonomous vehicle research. However, these datasets are usually collected from a single vehicle's one-time pass of a certain location, lacking multiagent interactions or repeated traversals of the same place. Such information could lead to transformative enhancements in autonomous vehicles' perception, prediction, and planning capabilities. To bridge this gap, in collaboration with the self-driving company May Mobility, we present the MARS dataset which unifies scenarios that enable MultiAgent, multitraveRSal, and multimodal autonomous vehicle research. More specifically, MARS is collected with a fleet of autonomous vehicles driving within a certain geographical area. Each vehicle has its own route and different vehicles may appear at nearby locations. Each vehicle is equipped with a LiDAR and surround-view RGB cameras. We curate two subsets in MARS: one facilitates collaborative driving with multiple vehicles simultaneously present at the same location, and the other enables memory retrospection through asynchronous traversals of the same location by multiple vehicles. We conduct experiments in place recognition and neural reconstruction. More importantly, MARS introduces new research opportunities and challenges such as multitraversal 3D reconstruction, multiagent perception, and unsupervised object discovery. Our data and codes can be found at https://ai4ce.github.io/MARS/.

Spatio-temporal reasoning is essential in understanding real-world environments in various fields, eg, autonomous driving and sports analytics. Recent advances have improved the spatial reasoning ability of Vision-Language Models (VLMs) by introducing large-scale data, but these models still struggle to analyze kinematic elements like traveled distance and speed of moving objects. To bridge this gap, we construct a spatio-temporal reasoning dataset and benchmark involving kinematic instruction tuning, referred to as STKit and STKit-Bench. They consist of real-world videos with 3D annotations, detailing object motion dynamics: traveled distance, speed, movement direction, inter-object distance comparisons, and relative movement direction. To further scale such data construction to videos without 3D labels, we propose an automatic pipeline to generate pseudo-labels using 4D reconstruction in real-world scale. With our kinematic instruction tuning data for spatio-temporal reasoning, we present ST-VLM, a VLM enhanced for spatio-temporal reasoning, which exhibits outstanding performance on STKit-Bench. Furthermore, we show that ST-VLM generalizes robustly across diverse domains and tasks, outperforming baselines on other spatio-temporal benchmarks (eg, ActivityNet, TVQA+). Finally, by integrating learned spatio-temporal reasoning with existing abilities, ST-VLM enables complex multi-step reasoning. Project page: https://ikodoh.github.io/ST-VLM.

Multi-agent trajectory prediction at signalized intersections is crucial for developing efficient intelligent transportation systems and safe autonomous driving systems. Due to the complexity of intersection scenarios and the limitations of single-vehicle perception, the performance of vehicle-centric prediction methods has reached a plateau. In this paper, we introduce an Infrastructure-to-Everything (I2X) collaborative prediction scheme. In this scheme, roadside units (RSUs) independently forecast the future trajectories of all vehicles and transmit these predictions unidirectionally to subscribing vehicles. Building on this scheme, we propose I2XTraj, a dedicated infrastructure-based trajectory prediction model. I2XTraj leverages real-time traffic signal states, prior maneuver strategy knowledge, and multi-agent interactions to generate accurate, joint multi-modal trajectory prediction. First, a continuous signal-informed mechanism is proposed to adaptively process real-time traffic signals to guide trajectory proposal generation under varied intersection configurations. Second, a driving strategy awareness mechanism estimates the joint distribution of maneuver strategies by integrating spatial priors of intersection areas with dynamic vehicle states, enabling coverage of the full set of feasible maneuvers. Third, a spatial-temporal-mode attention network models multi-agent interactions to refine and adjust joint trajectory outputs.Finally, I2XTraj is evaluated on two real-world datasets of signalized intersections, the V2X-Seq and the SinD drone dataset. In both single-infrastructure and online collaborative scenarios, our model outperforms state-of-the-art methods by over 30\% on V2X-Seq and 15\% on SinD, demonstrating strong generalizability and robustness.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

Learning a human-like driving policy from large-scale driving demonstrations is promising, but the uncertainty and non-deterministic nature of planning make it challenging. In this work, to cope with the uncertainty problem, we propose VADv2, an end-to-end driving model based on probabilistic planning. VADv2 takes multi-view image sequences as input in a streaming manner, transforms sensor data into environmental token embeddings, outputs the probabilistic distribution of action, and samples one action to control the vehicle. Only with camera sensors, VADv2 achieves state-of-the-art closed-loop performance on the CARLA Town05 benchmark, significantly outperforming all existing methods. It runs stably in a fully end-to-end manner, even without the rule-based wrapper. Closed-loop demos are presented at https://hgao-cv.github.io/VADv2.

Heterogeneity in sensors and actuators across environments poses a significant challenge to building large-scale pre-trained world models on top of this low-dimensional sensor information. In this work, we explore pre-training world models for heterogeneous environments by addressing key transfer barriers in both data diversity and model flexibility. We introduce UniTraj, a unified dataset comprising over one million trajectories from 80 environments, designed to scale data while preserving critical diversity. Additionally, we propose TrajWorld, a novel architecture capable of flexibly handling varying sensor and actuator information and capturing environment dynamics in-context. Pre-training TrajWorld on UniTraj demonstrates significant improvements in transition prediction and achieves a new state-of-the-art for off-policy evaluation. To the best of our knowledge, this work, for the first time, demonstrates the transfer benefits of world models across heterogeneous and complex control environments.

This paper tackles the challenge of real-time 3D trajectory prediction for UAVs, which is critical for applications such as aerial surveillance and defense. Existing prediction models that rely primarily on position data struggle with accuracy, especially when UAV movements fall outside the position domain used in training. Our research identifies a gap in utilizing velocity estimates, first-order dynamics, to better capture the dynamics and enhance prediction accuracy and generalizability in any position domain. To bridge this gap, we propose a new trajectory prediction method using Gated Recurrent Units (GRUs) within sequence-based neural networks. Unlike traditional methods that rely on RNNs or transformers, this approach forecasts future velocities and positions based on historical velocity data instead of positions. This is designed to enhance prediction accuracy and scalability, overcoming challenges faced by conventional models in handling complex UAV dynamics. The methodology employs both synthetic and real-world 3D UAV trajectory data, capturing a wide range of flight patterns, speeds, and agility. Synthetic data is generated using the Gazebo simulator and PX4 Autopilot, while real-world data comes from the UZH-FPV and Mid-Air drone racing datasets. The GRU-based models significantly outperform state-of-the-art RNN approaches, with a mean square error (MSE) as low as 2 x 10^-8. Overall, our findings confirm the effectiveness of incorporating velocity data in improving the accuracy of UAV trajectory predictions across both synthetic and real-world scenarios, in and out of position data distributions. Finally, we open-source our 5000 trajectories dataset and a ROS 2 package to facilitate the integration with existing ROS-based UAV systems.

Autonomous driving (AD) systems struggle in long-tail scenarios due to limited world knowledge and weak visual dynamic modeling. Existing vision-language-action (VLA)-based methods cannot leverage unlabeled videos for visual causal learning, while world model-based methods lack reasoning capabilities from large language models. In this paper, we construct multiple specialized datasets providing reasoning and planning annotations for complex scenarios. Then, a unified Understanding-Generation-Planning framework, named UniUGP, is proposed to synergize scene reasoning, future video generation, and trajectory planning through a hybrid expert architecture. By integrating pre-trained VLMs and video generation models, UniUGP leverages visual dynamics and semantic reasoning to enhance planning performance. Taking multi-frame observations and language instructions as input, it produces interpretable chain-of-thought reasoning, physically consistent trajectories, and coherent future videos. We introduce a four-stage training strategy that progressively builds these capabilities across multiple existing AD datasets, along with the proposed specialized datasets. Experiments demonstrate state-of-the-art performance in perception, reasoning, and decision-making, with superior generalization to challenging long-tail situations.

Predicting future trajectories for other road agents is an essential task for autonomous vehicles. Established trajectory prediction methods primarily use agent tracks generated by a detection and tracking system and HD map as inputs. In this work, we propose a novel method that also incorporates visual input from surround-view cameras, allowing the model to utilize visual cues such as human gazes and gestures, road conditions, vehicle turn signals, etc, which are typically hidden from the model in prior methods. Furthermore, we use textual descriptions generated by a Vision-Language Model (VLM) and refined by a Large Language Model (LLM) as supervision during training to guide the model on what to learn from the input data. Despite using these extra inputs, our method achieves a latency of 53 ms, making it feasible for real-time processing, which is significantly faster than that of previous single-agent prediction methods with similar performance. Our experiments show that both the visual inputs and the textual descriptions contribute to improvements in trajectory prediction performance, and our qualitative analysis highlights how the model is able to exploit these additional inputs. Lastly, in this work we create and release the nuScenes-Text dataset, which augments the established nuScenes dataset with rich textual annotations for every scene, demonstrating the positive impact of utilizing VLM on trajectory prediction. Our project page is at https://moonseokha.github.io/VisionTrap/

Autonomous vehicles operate in highly dynamic environments necessitating an accurate assessment of which aspects of a scene are moving and where they are moving to. A popular approach to 3D motion estimation, termed scene flow, is to employ 3D point cloud data from consecutive LiDAR scans, although such approaches have been limited by the small size of real-world, annotated LiDAR data. In this work, we introduce a new large-scale dataset for scene flow estimation derived from corresponding tracked 3D objects, which is sim1,000times larger than previous real-world datasets in terms of the number of annotated frames. We demonstrate how previous works were bounded based on the amount of real LiDAR data available, suggesting that larger datasets are required to achieve state-of-the-art predictive performance. Furthermore, we show how previous heuristics for operating on point clouds such as down-sampling heavily degrade performance, motivating a new class of models that are tractable on the full point cloud. To address this issue, we introduce the FastFlow3D architecture which provides real time inference on the full point cloud. Additionally, we design human-interpretable metrics that better capture real world aspects by accounting for ego-motion and providing breakdowns per object type. We hope that this dataset may provide new opportunities for developing real world scene flow systems.

Safety and robustness are crucial factors in developing trustworthy autonomous vehicles. One essential aspect of addressing these factors is to equip vehicles with the capability to predict future trajectories for all moving objects in the surroundings and quantify prediction uncertainties. In this paper, we propose the Sequential Neural Variational Agent (SeNeVA), a generative model that describes the distribution of future trajectories for a single moving object. Our approach can distinguish Out-of-Distribution data while quantifying uncertainty and achieving competitive performance compared to state-of-the-art methods on the Argoverse 2 and INTERACTION datasets. Specifically, a 0.446 meters minimum Final Displacement Error, a 0.203 meters minimum Average Displacement Error, and a 5.35% Miss Rate are achieved on the INTERACTION test set. Extensive qualitative and quantitative analysis is also provided to evaluate the proposed model. Our open-source code is available at https://github.com/PurdueDigitalTwin/seneva.

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

Multi-object tracking (MOT) has traditionally focused on estimating trajectories of all objects in a video, without selectively reasoning about user-specified targets under semantic instructions. In this work, we introduce a query-driven tracking paradigm that formulates tracking as a spatiotemporal reasoning problem conditioned on natural language queries. Given a reference frame, a video sequence, and a textual query, the goal is to localize and track only the target(s) specified in the query while maintaining temporal coherence and identity consistency. To support this setting, we construct RMOT26, a large-scale benchmark with grounded queries and sequence-level splits to prevent identity leakage and enable robust evaluation of generalization. We further present QTrack, an end-to-end vision-language model that integrates multimodal reasoning with tracking-oriented localization. Additionally, we introduce a Temporal Perception-Aware Policy Optimization strategy with structured rewards to encourage motion-aware reasoning. Extensive experiments demonstrate the effectiveness of our approach for reasoning-centric, language-guided tracking. Code and data are available at https://github.com/gaash-lab/QTrack

Predicting the motion of multiple traffic participants has always been one of the most challenging tasks in autonomous driving. The recently proposed occupancy flow field prediction method has shown to be a more effective and scalable representation compared to general trajectory prediction methods. However, in complex multi-agent traffic scenarios, it remains difficult to model the interactions among various factors and the dependencies among prediction outputs at different time steps. In view of this, we propose a transformer-based hierarchical feature guided network (HGNET), which can efficiently extract features of agents and map information from visual and vectorized inputs, modeling multimodal interaction relationships. Second, we design the Feature-Guided Attention (FGAT) module to leverage the potential guiding effects between different prediction targets, thereby improving prediction accuracy. Additionally, to enhance the temporal consistency and causal relationships of the predictions, we propose a Time Series Memory framework to learn the conditional distribution models of the prediction outputs at future time steps from multivariate time series. The results demonstrate that our model exhibits competitive performance, which ranks 3rd in the 2024 Waymo Occupancy and Flow Prediction Challenge.

With the advanced request to employ a team of robots to perform a task collaboratively, the research community has become increasingly interested in collaborative simultaneous localization and mapping. Unfortunately, existing datasets are limited in the scale and variation of the collaborative trajectories, even though generalization between inter-trajectories among different agents is crucial to the overall viability of collaborative tasks. To help align the research community's contributions with realistic multiagent ordinated SLAM problems, we propose S3E, a large-scale multimodal dataset captured by a fleet of unmanned ground vehicles along four designed collaborative trajectory paradigms. S3E consists of 7 outdoor and 5 indoor sequences that each exceed 200 seconds, consisting of well temporal synchronized and spatial calibrated high-frequency IMU, high-quality stereo camera, and 360 degree LiDAR data. Crucially, our effort exceeds previous attempts regarding dataset size, scene variability, and complexity. It has 4x as much average recording time as the pioneering EuRoC dataset. We also provide careful dataset analysis as well as baselines for collaborative SLAM and single counterparts. Data and more up-to-date details are found at https://github.com/PengYu-Team/S3E.

Predicting the motion of other agents in a scene is highly relevant for autonomous driving, as it allows a self-driving car to anticipate. Inspired by the success of decoder-only models for language modeling, we propose DONUT, a Decoder-Only Network for Unrolling Trajectories. Unlike existing encoder-decoder forecasting models, we encode historical trajectories and predict future trajectories with a single autoregressive model. This allows the model to make iterative predictions in a consistent manner, and ensures that the model is always provided with up-to-date information, thereby enhancing performance. Furthermore, inspired by multi-token prediction for language modeling, we introduce an 'overprediction' strategy that gives the model the auxiliary task of predicting trajectories at longer temporal horizons. This allows the model to better anticipate the future and further improves performance. Through experiments, we demonstrate that our decoder-only approach outperforms the encoder-decoder baseline, and achieves new state-of-the-art results on the Argoverse 2 single-agent motion forecasting benchmark.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Predicting future motion is crucial in video understanding and controllable video generation. Dense point trajectories are a compact, expressive motion representation, but modeling their future evolution from observed video remains challenging. We propose a framework that predicts future trajectories and visibility from past trajectories and video context. Our method has three components: (1) Grid-Anchor Offset Encoding, which reduces location-dependent bias by representing each point as an offset from its pixel-center anchor; (2) TrajLoom-VAE, which learns a compact spatiotemporal latent space for dense trajectories with masked reconstruction and a spatiotemporal consistency regularizer; and (3) TrajLoom-Flow, which generates future trajectories in latent space via flow matching, with boundary cues and on-policy K-step fine-tuning for stable sampling. We also introduce TrajLoomBench, a unified benchmark spanning real and synthetic videos with a standardized setup aligned with video-generation benchmarks. Compared with state-of-the-art methods, our approach extends the prediction horizon from 24 to 81 frames while improving motion realism and stability across datasets. The predicted trajectories directly support downstream video generation and editing. Code, model checkpoints, and datasets are available at https://trajloom.github.io/.

Recent video generation approaches increasingly rely on planning intermediate control signals such as object trajectories to improve temporal coherence and motion fidelity. However, these methods mostly employ single-shot plans that are typically limited to simple motions, or iterative refinement which requires multiple calls to the video generator, incuring high computational cost. To overcome these limitations, we propose SketchVerify, a training-free, sketch-verification-based planning framework that improves motion planning quality with more dynamically coherent trajectories (i.e., physically plausible and instruction-consistent motions) prior to full video generation by introducing a test-time sampling and verification loop. Given a prompt and a reference image, our method predicts multiple candidate motion plans and ranks them using a vision-language verifier that jointly evaluates semantic alignment with the instruction and physical plausibility. To efficiently score candidate motion plans, we render each trajectory as a lightweight video sketch by compositing objects over a static background, which bypasses the need for expensive, repeated diffusion-based synthesis while achieving comparable performance. We iteratively refine the motion plan until a satisfactory one is identified, which is then passed to the trajectory-conditioned generator for final synthesis. Experiments on WorldModelBench and PhyWorldBench demonstrate that our method significantly improves motion quality, physical realism, and long-term consistency compared to competitive baselines while being substantially more efficient. Our ablation study further shows that scaling up the number of trajectory candidates consistently enhances overall performance.

We identify a fundamental Narrow Policy limitation undermining the performance of autonomous VLA models, where driving Imitation Learning (IL) tends to collapse exploration and limit the potential of subsequent Reinforcement Learning (RL) stages, which often saturate prematurely due to insufficient feedback diversity. Thereby, we propose Curious-VLA, a framework that alleviates the exploit-explore dilemma through a two-stage design. During IL, we introduce a Feasible Trajectory Expansion (FTE) strategy to generate multiple physically valid trajectories and a step-wise normalized trajectory representation to adapt this diverse data. In the RL stage, we present Adaptive Diversity-Aware Sampling (ADAS) that prioritizes high-diversity samples and introduce Spanning Driving Reward (SDR) with a focal style weighting to amplify reward's value span for improving sensitivity to driving quality. On the Navsim benchmark, Curious-VLA achieves SoTA results (PDMS 90.3, EPDMS 85.4) and a Best-of-N PDMS of 94.8, demonstrating its effectiveness in unlocking the exploratory potential of VLA models. Code: https://github.com/Mashiroln/curious_vla.git.

The field of multi-object tracking has recently seen a renewed interest in the good old schema of tracking-by-detection, as its simplicity and strong priors spare it from the complex design and painful babysitting of tracking-by-attention approaches. In view of this, we aim at extending tracking-by-detection to multi-modal settings, where a comprehensive cost has to be computed from heterogeneous information e.g., 2D motion cues, visual appearance, and pose estimates. More precisely, we follow a case study where a rough estimate of 3D information is also available and must be merged with other traditional metrics (e.g., the IoU). To achieve that, recent approaches resort to either simple rules or complex heuristics to balance the contribution of each cost. However, i) they require careful tuning of tailored hyperparameters on a hold-out set, and ii) they imply these costs to be independent, which does not hold in reality. We address these issues by building upon an elegant probabilistic formulation, which considers the cost of a candidate association as the negative log-likelihood yielded by a deep density estimator, trained to model the conditional joint probability distribution of correct associations. Our experiments, conducted on both simulated and real benchmarks, show that our approach consistently enhances the performance of several tracking-by-detection algorithms.

Vision Language Models (VLMs) bridge visual perception and linguistic reasoning. In Autonomous Driving (AD), this synergy has enabled Vision Language Action (VLA) models, which translate high-level multimodal understanding into driving behaviors, typically represented as future trajectories. However, existing VLA models mainly generate generic collision-free trajectories. Beyond collision avoidance, adapting to diverse driving styles (e.g., sporty, comfortable) is essential for personalized driving. Moreover, many methods treat trajectory generation as naive token prediction, which can produce kinematically infeasible actions. To address these limitations, we present StyleVLA, a physics-informed VLA framework for generating diverse and physically plausible driving behaviors. We introduce a hybrid loss that combines a kinematic consistency constraint with a continuous regression head to improve trajectory feasibility. To train StyleVLA, built on Qwen3-VL-4B, we construct a large-scale instruction dataset with over 1.2k scenarios, 76k Bird's Eye View (BEV) samples, and 42k First Person View (FPV) samples, with ground-truth trajectories for five driving styles and natural-language instructions. Experiments show that our 4B-parameter StyleVLA significantly outperforms proprietary models (e.g., Gemini-3-Pro) and state-of-the-art VLA models. Using a composite driving score measuring success rate, physical feasibility, and style adherence, StyleVLA achieves 0.55 on BEV and 0.51 on FPV, versus 0.32 and 0.35 for Gemini-3-Pro. These results show that a specialized, physics-informed, lightweight model can surpass closed-source models on domain-specific tasks.

Accurate long-horizon vessel trajectory prediction remains challenging due to compounded uncertainty from complex navigation behaviors and environmental factors. Existing methods often struggle to maintain global directional consistency, leading to drifting or implausible trajectories when extrapolated over long time horizons. To address this issue, we propose a semantic-key-point-conditioned trajectory modeling framework, in which future trajectories are predicted by conditioning on a high-level Next Key Point (NKP) that captures navigational intent. This formulation decomposes long-horizon prediction into global semantic decision-making and local motion modeling, effectively restricting the support of future trajectories to semantically feasible subsets. To efficiently estimate the NKP prior from historical observations, we adopt a pretrain-finetune strategy. Extensive experiments on real-world AIS data demonstrate that the proposed method consistently outperforms state-of-the-art approaches, particularly for long travel durations, directional accuracy, and fine-grained trajectory prediction.

Humans can predict future human trajectories even from momentary observations by using human pose-related cues. However, previous Human Trajectory Prediction (HTP) methods leverage the pose cues implicitly, resulting in implausible predictions. To address this, we propose Locomotion Embodiment, a framework that explicitly evaluates the physical plausibility of the predicted trajectory by locomotion generation under the laws of physics. While the plausibility of locomotion is learned with an indifferentiable physics simulator, it is replaced by our differentiable Locomotion Value function to train an HTP network in a data-driven manner. In particular, our proposed Embodied Locomotion loss is beneficial for efficiently training a stochastic HTP network using multiple heads. Furthermore, the Locomotion Value filter is proposed to filter out implausible trajectories at inference. Experiments demonstrate that our method enhances even the state-of-the-art HTP methods across diverse datasets and problem settings. Our code is available at: https://github.com/ImIntheMiddle/EmLoco.

The ability to accurately predict the trajectory of surrounding vehicles is a critical hurdle to overcome on the journey to fully autonomous vehicles. To address this challenge, we pioneer a novel behavior-aware trajectory prediction model (BAT) that incorporates insights and findings from traffic psychology, human behavior, and decision-making. Our model consists of behavior-aware, interaction-aware, priority-aware, and position-aware modules that perceive and understand the underlying interactions and account for uncertainty and variability in prediction, enabling higher-level learning and flexibility without rigid categorization of driving behavior. Importantly, this approach eliminates the need for manual labeling in the training process and addresses the challenges of non-continuous behavior labeling and the selection of appropriate time windows. We evaluate BAT's performance across the Next Generation Simulation (NGSIM), Highway Drone (HighD), Roundabout Drone (RounD), and Macao Connected Autonomous Driving (MoCAD) datasets, showcasing its superiority over prevailing state-of-the-art (SOTA) benchmarks in terms of prediction accuracy and efficiency. Remarkably, even when trained on reduced portions of the training data (25%), our model outperforms most of the baselines, demonstrating its robustness and efficiency in predicting vehicle trajectories, and the potential to reduce the amount of data required to train autonomous vehicles, especially in corner cases. In conclusion, the behavior-aware model represents a significant advancement in the development of autonomous vehicles capable of predicting trajectories with the same level of proficiency as human drivers. The project page is available at https://github.com/Petrichor625/BATraj-Behavior-aware-Model.

Flight trajectory data plays a vital role in the traffic management community, especially for downstream tasks such as trajectory prediction, flight recognition, and anomaly detection. Existing works often utilize handcrafted features and design models for different tasks individually, which heavily rely on domain expertise and are hard to extend. We argue that different flight analysis tasks share the same useful features of the trajectory. Jointly learning a unified representation for flight trajectories could be beneficial for improving the performance of various tasks. However, flight trajectory representation learning (TRL) faces two primary challenges, \ie unbalanced behavior density and 3D spatial continuity, which disable recent general TRL methods. In this paper, we propose Flight2Vec , a flight-specific representation learning method to address these challenges. Specifically, a behavior-adaptive patching mechanism is used to inspire the learned representation to pay more attention to behavior-dense segments. Moreover, we introduce a motion trend learning technique that guides the model to memorize not only the precise locations, but also the motion trend to generate better representations. Extensive experimental results demonstrate that Flight2Vec significantly improves performance in downstream tasks such as flight trajectory prediction, flight recognition, and anomaly detection.

3D multi-object tracking (MOT) is vital for many applications including autonomous driving vehicles and service robots. With the commonly used tracking-by-detection paradigm, 3D MOT has made important progress in recent years. However, these methods only use the detection boxes of the current frame to obtain trajectory-box association results, which makes it impossible for the tracker to recover objects missed by the detector. In this paper, we present TrajectoryFormer, a novel point-cloud-based 3D MOT framework. To recover the missed object by detector, we generates multiple trajectory hypotheses with hybrid candidate boxes, including temporally predicted boxes and current-frame detection boxes, for trajectory-box association. The predicted boxes can propagate object's history trajectory information to the current frame and thus the network can tolerate short-term miss detection of the tracked objects. We combine long-term object motion feature and short-term object appearance feature to create per-hypothesis feature embedding, which reduces the computational overhead for spatial-temporal encoding. Additionally, we introduce a Global-Local Interaction Module to conduct information interaction among all hypotheses and models their spatial relations, leading to accurate estimation of hypotheses. Our TrajectoryFormer achieves state-of-the-art performance on the Waymo 3D MOT benchmarks. Code is available at https://github.com/poodarchu/EFG .

Accurate and efficient modeling of agent interactions is essential for trajectory generation, the core of autonomous driving systems. Existing methods, scene-centric, agent-centric, and query-centric frameworks, each present distinct advantages and drawbacks, creating an impossible triangle among accuracy, computational time, and memory efficiency. To break this limitation, we propose Directional Rotary Position Embedding (DRoPE), a novel adaptation of Rotary Position Embedding (RoPE), originally developed in natural language processing. Unlike traditional relative position embedding (RPE), which introduces significant space complexity, RoPE efficiently encodes relative positions without explicitly increasing complexity but faces inherent limitations in handling angular information due to periodicity. DRoPE overcomes this limitation by introducing a uniform identity scalar into RoPE's 2D rotary transformation, aligning rotation angles with realistic agent headings to naturally encode relative angular information. We theoretically analyze DRoPE's correctness and efficiency, demonstrating its capability to simultaneously optimize trajectory generation accuracy, time complexity, and space complexity. Empirical evaluations compared with various state-of-the-art trajectory generation models, confirm DRoPE's good performance and significantly reduced space complexity, indicating both theoretical soundness and practical effectiveness. The video documentation is available at https://drope-traj.github.io/.

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (Principled and Efficient Test-TimeSelf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the self-consistency rate, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to 75% (offline) and 55% (online) relative to uniform allocation. Code is available at https://github.com/ZDCSlab/PETS.

Effective spatio-temporal representation is fundamental to modeling, understanding, and predicting dynamics in videos. The atomic unit of a video, the pixel, traces a continuous 3D trajectory over time, serving as the primitive element of dynamics. Based on this principle, we propose representing any video as a Trajectory Field: a dense mapping that assigns a continuous 3D trajectory function of time to each pixel in every frame. With this representation, we introduce Trace Anything, a neural network that predicts the entire trajectory field in a single feed-forward pass. Specifically, for each pixel in each frame, our model predicts a set of control points that parameterizes a trajectory (i.e., a B-spline), yielding its 3D position at arbitrary query time instants. We trained the Trace Anything model on large-scale 4D data, including data from our new platform, and our experiments demonstrate that: (i) Trace Anything achieves state-of-the-art performance on our new benchmark for trajectory field estimation and performs competitively on established point-tracking benchmarks; (ii) it offers significant efficiency gains thanks to its one-pass paradigm, without requiring iterative optimization or auxiliary estimators; and (iii) it exhibits emergent abilities, including goal-conditioned manipulation, motion forecasting, and spatio-temporal fusion. Project page: https://trace-anything.github.io/.

A reliable and accurate 3D tracking framework is essential for predicting future locations of surrounding objects and planning the observer's actions in numerous applications such as autonomous driving. We propose a framework that can effectively associate moving objects over time and estimate their full 3D bounding box information from a sequence of 2D images captured on a moving platform. The object association leverages quasi-dense similarity learning to identify objects in various poses and viewpoints with appearance cues only. After initial 2D association, we further utilize 3D bounding boxes depth-ordering heuristics for robust instance association and motion-based 3D trajectory prediction for re-identification of occluded vehicles. In the end, an LSTM-based object velocity learning module aggregates the long-term trajectory information for more accurate motion extrapolation. Experiments on our proposed simulation data and real-world benchmarks, including KITTI, nuScenes, and Waymo datasets, show that our tracking framework offers robust object association and tracking on urban-driving scenarios. On the Waymo Open benchmark, we establish the first camera-only baseline in the 3D tracking and 3D detection challenges. Our quasi-dense 3D tracking pipeline achieves impressive improvements on the nuScenes 3D tracking benchmark with near five times tracking accuracy of the best vision-only submission among all published methods. Our code, data and trained models are available at https://github.com/SysCV/qd-3dt.

Long-term planning for robots operating in domestic environments poses unique challenges due to the interactions between humans, objects, and spaces. Recent advancements in trajectory planning have leveraged vision-language models (VLMs) to extract contextual information for robots operating in real-world environments. While these methods achieve satisfying performance, they do not explicitly model human activities. Such activities influence surrounding objects and reshape spatial constraints. This paper presents a novel approach to trajectory planning that integrates human preferences, activities, and spatial context through an enriched 3D scene graph (3DSG) representation. By incorporating activity-based relationships, our method captures the spatial impact of human actions, leading to more context-sensitive trajectory adaptation. Preliminary results demonstrate that our approach effectively assigns costs to spaces influenced by human activities, ensuring that the robot trajectory remains contextually appropriate and sensitive to the ongoing environment. This balance between task efficiency and social appropriateness enhances context-aware human-robot interactions in domestic settings. Future work includes implementing a full planning pipeline and conducting user studies to evaluate trajectory acceptability.