Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra
Abstract
Generative Anchored Fields learns independent noise and data predictors from linear bridges to enable compositional control through transport algebra and efficient high-quality generation.
We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, J (noise) and K (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate learning. The velocity field v=K-J emerges from their time-conditioned disagreement. This factorization enables Transport Algebra: algebraic operations on multiple J/K heads for compositional control. With class-specific K_n heads, GAF defines directed transport maps between a shared base noise distribution and multiple data domains, allowing controllable interpolation, multi-class composition, and semantic editing. This is achieved either directly on the predicted data coordinates (K) using Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in 5-8 steps, or on the emergent velocity field (v). We achieve strong sample quality (FID 7.51 on ImageNet 256times256 and 7.27 on CelebA-HQ 256times 256, without classifier-free guidance) while treating compositional generation as an architectural primitive. Code available at https://github.com/IDLabMedia/GAF.
Community
Introducing Generative Anchored Fields (GAF).
Paper: https://arxiv.org/abs/2511.22693v2
Code: https://github.com/IDLabMedia/GAF
GAF learns independent endpoint predictors, J (noise) and K (data).
Instead of predicting v(x,t) directly (e.g., flow matching), GAF predicts where the trajectory starts (J) and where it ends (K).
The velocity emerges as v=K-J. This enables Transport Algebra: algebraic operations on J/K heads for compositional generation. In GAF, the transport is derived from endpoint disagreement, not trained as a standalone trajectory predictor.
In practice, this enables:
Interpolating between classes, switching manifolds mid-trajectory, combining heads for novel generation, without extra training, or guidance.
We also introduce Iterative Endpoint Refinement (IER), a native GAF sampler that iteratively refines the endpoints in forward and reverse directions. IER generates high-quality images with 5-8 steps.
Without classifier-free guidance:
FID 7.51 on ImageNet 256×256 (retrunked from DiT-XL/2 in only 100k steps)
FID 7.27 on CelebA-HQ 256×256 (trained from scratch)
Training GAF is simple: endpoint regression + residual and swap regularizers. Sampling is deterministic and guidance-free.
Models citing this paper 0
No model linking this paper
Datasets citing this paper 0
No dataset linking this paper
Spaces citing this paper 0
No Space linking this paper
Collections including this paper 0
No Collection including this paper