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extensions_built_in/diffusion_models/hidream/src/schedulers/fm_solvers_unipc.py

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+# Copied from https://github.com/huggingface/diffusers/blob/v0.31.0/src/diffusers/schedulers/scheduling_unipc_multistep.py
+# Convert unipc for flow matching
+# Copyright 2024-2025 The Alibaba Wan Team Authors. All rights reserved.
+
+import math
+from typing import List, Optional, Tuple, Union
+
+import numpy as np
+import torch
+from diffusers.configuration_utils import ConfigMixin, register_to_config
+from diffusers.schedulers.scheduling_utils import (KarrasDiffusionSchedulers,
+                                                   SchedulerMixin,
+                                                   SchedulerOutput)
+from diffusers.utils import deprecate, is_scipy_available
+
+if is_scipy_available():
+    import scipy.stats
+
+
+class FlowUniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
+    """
+    `UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.
+
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
+
+    Args:
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        solver_order (`int`, default `2`):
+            The UniPC order which can be any positive integer. The effective order of accuracy is `solver_order + 1`
+            due to the UniC. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for
+            unconditional sampling.
+        prediction_type (`str`, defaults to "flow_prediction"):
+            Prediction type of the scheduler function; must be `flow_prediction` for this scheduler, which predicts
+            the flow of the diffusion process.
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True` and `predict_x0=True`.
+        predict_x0 (`bool`, defaults to `True`):
+            Whether to use the updating algorithm on the predicted x0.
+        solver_type (`str`, default `bh2`):
+            Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
+            otherwise.
+        lower_order_final (`bool`, default `True`):
+            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
+            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
+        disable_corrector (`list`, default `[]`):
+            Decides which step to disable the corrector to mitigate the misalignment between `epsilon_theta(x_t, c)`
+            and `epsilon_theta(x_t^c, c)` which can influence convergence for a large guidance scale. Corrector is
+            usually disabled during the first few steps.
+        solver_p (`SchedulerMixin`, default `None`):
+            Any other scheduler that if specified, the algorithm becomes `solver_p + UniC`.
+        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
+            the sigmas are determined according to a sequence of noise levels {σi}.
+        use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
+        timestep_spacing (`str`, defaults to `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
+            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        steps_offset (`int`, defaults to 0):
+            An offset added to the inference steps, as required by some model families.
+        final_sigmas_type (`str`, defaults to `"zero"`):
+            The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
+            sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
+    """
+
+    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
+    order = 1
+
+    @register_to_config
+    def __init__(
+            self,
+            num_train_timesteps: int = 1000,
+            solver_order: int = 2,
+            prediction_type: str = "flow_prediction",
+            shift: Optional[float] = 1.0,
+            use_dynamic_shifting=False,
+            thresholding: bool = False,
+            dynamic_thresholding_ratio: float = 0.995,
+            sample_max_value: float = 1.0,
+            predict_x0: bool = True,
+            solver_type: str = "bh2",
+            lower_order_final: bool = True,
+            disable_corrector: List[int] = [],
+            solver_p: SchedulerMixin = None,
+            timestep_spacing: str = "linspace",
+            steps_offset: int = 0,
+            final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
+    ):
+
+        if solver_type not in ["bh1", "bh2"]:
+            if solver_type in ["midpoint", "heun", "logrho"]:
+                self.register_to_config(solver_type="bh2")
+            else:
+                raise NotImplementedError(
+                    f"{solver_type} is not implemented for {self.__class__}")
+
+        self.predict_x0 = predict_x0
+        # setable values
+        self.num_inference_steps = None
+        alphas = np.linspace(1, 1 / num_train_timesteps,
+                             num_train_timesteps)[::-1].copy()
+        sigmas = 1.0 - alphas
+        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32)
+
+        if not use_dynamic_shifting:
+            # when use_dynamic_shifting is True, we apply the timestep shifting on the fly based on the image resolution
+            sigmas = shift * sigmas / (1 +
+                                       (shift - 1) * sigmas)  # pyright: ignore
+
+        self.sigmas = sigmas
+        self.timesteps = sigmas * num_train_timesteps
+
+        self.model_outputs = [None] * solver_order
+        self.timestep_list = [None] * solver_order
+        self.lower_order_nums = 0
+        self.disable_corrector = disable_corrector
+        self.solver_p = solver_p
+        self.last_sample = None
+        self._step_index = None
+        self._begin_index = None
+
+        self.sigmas = self.sigmas.to(
+            "cpu")  # to avoid too much CPU/GPU communication
+        self.sigma_min = self.sigmas[-1].item()
+        self.sigma_max = self.sigmas[0].item()
+
+    @property
+    def step_index(self):
+        """
+        The index counter for current timestep. It will increase 1 after each scheduler step.
+        """
+        return self._step_index
+
+    @property
+    def begin_index(self):
+        """
+        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
+        """
+        return self._begin_index
+
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
+    def set_begin_index(self, begin_index: int = 0):
+        """
+        Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
+
+        Args:
+            begin_index (`int`):
+                The begin index for the scheduler.
+        """
+        self._begin_index = begin_index
+
+    # Modified from diffusers.schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteScheduler.set_timesteps
+    def set_timesteps(
+        self,
+        num_inference_steps: Union[int, None] = None,
+        device: Union[str, torch.device] = None,
+        sigmas: Optional[List[float]] = None,
+        mu: Optional[Union[float, None]] = None,
+        shift: Optional[Union[float, None]] = None,
+    ):
+        """
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
+        Args:
+            num_inference_steps (`int`):
+                Total number of the spacing of the time steps.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+        """
+
+        if self.config.use_dynamic_shifting and mu is None:
+            raise ValueError(
+                " you have to pass a value for `mu` when `use_dynamic_shifting` is set to be `True`"
+            )
+
+        if sigmas is None:
+            sigmas = np.linspace(self.sigma_max, self.sigma_min,
+                                 num_inference_steps +
+                                 1).copy()[:-1]  # pyright: ignore
+
+        if self.config.use_dynamic_shifting:
+            sigmas = self.time_shift(mu, 1.0, sigmas)  # pyright: ignore
+        else:
+            if shift is None:
+                shift = self.config.shift
+            sigmas = shift * sigmas / (1 +
+                                       (shift - 1) * sigmas)  # pyright: ignore
+
+        if self.config.final_sigmas_type == "sigma_min":
+            sigma_last = ((1 - self.alphas_cumprod[0]) /
+                          self.alphas_cumprod[0])**0.5
+        elif self.config.final_sigmas_type == "zero":
+            sigma_last = 0
+        else:
+            raise ValueError(
+                f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
+            )
+
+        timesteps = sigmas * self.config.num_train_timesteps
+        sigmas = np.concatenate([sigmas, [sigma_last]
+                                ]).astype(np.float32)  # pyright: ignore
+
+        self.sigmas = torch.from_numpy(sigmas)
+        self.timesteps = torch.from_numpy(timesteps).to(
+            device=device, dtype=torch.int64)
+
+        self.num_inference_steps = len(timesteps)
+
+        self.model_outputs = [
+            None,
+        ] * self.config.solver_order
+        self.lower_order_nums = 0
+        self.last_sample = None
+        if self.solver_p:
+            self.solver_p.set_timesteps(self.num_inference_steps, device=device)
+
+        # add an index counter for schedulers that allow duplicated timesteps
+        self._step_index = None
+        self._begin_index = None
+        self.sigmas = self.sigmas.to(
+            "cpu")  # to avoid too much CPU/GPU communication
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
+    def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
+        """
+        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
+        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
+        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
+        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
+        photorealism as well as better image-text alignment, especially when using very large guidance weights."
+
+        https://arxiv.org/abs/2205.11487
+        """
+        dtype = sample.dtype
+        batch_size, channels, *remaining_dims = sample.shape
+
+        if dtype not in (torch.float32, torch.float64):
+            sample = sample.float(
+            )  # upcast for quantile calculation, and clamp not implemented for cpu half
+
+        # Flatten sample for doing quantile calculation along each image
+        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
+
+        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"
+
+        s = torch.quantile(
+            abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
+        s = torch.clamp(
+            s, min=1, max=self.config.sample_max_value
+        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
+        s = s.unsqueeze(
+            1)  # (batch_size, 1) because clamp will broadcast along dim=0
+        sample = torch.clamp(
+            sample, -s, s
+        ) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"
+
+        sample = sample.reshape(batch_size, channels, *remaining_dims)
+        sample = sample.to(dtype)
+
+        return sample
+
+    # Copied from diffusers.schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteScheduler._sigma_to_t
+    def _sigma_to_t(self, sigma):
+        return sigma * self.config.num_train_timesteps
+
+    def _sigma_to_alpha_sigma_t(self, sigma):
+        return 1 - sigma, sigma
+
+    # Copied from diffusers.schedulers.scheduling_flow_match_euler_discrete.set_timesteps
+    def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
+        return math.exp(mu) / (math.exp(mu) + (1 / t - 1)**sigma)
+
+    def convert_model_output(
+        self,
+        model_output: torch.Tensor,
+        *args,
+        sample: torch.Tensor = None,
+        **kwargs,
+    ) -> torch.Tensor:
+        r"""
+        Convert the model output to the corresponding type the UniPC algorithm needs.
+
+        Args:
+            model_output (`torch.Tensor`):
+                The direct output from the learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by the diffusion process.
+
+        Returns:
+            `torch.Tensor`:
+                The converted model output.
+        """
+        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
+        if sample is None:
+            if len(args) > 1:
+                sample = args[1]
+            else:
+                raise ValueError(
+                    "missing `sample` as a required keyward argument")
+        if timestep is not None:
+            deprecate(
+                "timesteps",
+                "1.0.0",
+                "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
+            )
+
+        sigma = self.sigmas[self.step_index]
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+
+        if self.predict_x0:
+            if self.config.prediction_type == "flow_prediction":
+                sigma_t = self.sigmas[self.step_index]
+                x0_pred = sample - sigma_t * model_output
+            else:
+                raise ValueError(
+                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`,"
+                    " `v_prediction` or `flow_prediction` for the UniPCMultistepScheduler."
+                )
+
+            if self.config.thresholding:
+                x0_pred = self._threshold_sample(x0_pred)
+
+            return x0_pred
+        else:
+            if self.config.prediction_type == "flow_prediction":
+                sigma_t = self.sigmas[self.step_index]
+                epsilon = sample - (1 - sigma_t) * model_output
+            else:
+                raise ValueError(
+                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`,"
+                    " `v_prediction` or `flow_prediction` for the UniPCMultistepScheduler."
+                )
+
+            if self.config.thresholding:
+                sigma_t = self.sigmas[self.step_index]
+                x0_pred = sample - sigma_t * model_output
+                x0_pred = self._threshold_sample(x0_pred)
+                epsilon = model_output + x0_pred
+
+            return epsilon
+
+    def multistep_uni_p_bh_update(
+        self,
+        model_output: torch.Tensor,
+        *args,
+        sample: torch.Tensor = None,
+        order: int = None,  # pyright: ignore
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.
+
+        Args:
+            model_output (`torch.Tensor`):
+                The direct output from the learned diffusion model at the current timestep.
+            prev_timestep (`int`):
+                The previous discrete timestep in the diffusion chain.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by the diffusion process.
+            order (`int`):
+                The order of UniP at this timestep (corresponds to the *p* in UniPC-p).
+
+        Returns:
+            `torch.Tensor`:
+                The sample tensor at the previous timestep.
+        """
+        prev_timestep = args[0] if len(args) > 0 else kwargs.pop(
+            "prev_timestep", None)
+        if sample is None:
+            if len(args) > 1:
+                sample = args[1]
+            else:
+                raise ValueError(
+                    " missing `sample` as a required keyward argument")
+        if order is None:
+            if len(args) > 2:
+                order = args[2]
+            else:
+                raise ValueError(
+                    " missing `order` as a required keyward argument")
+        if prev_timestep is not None:
+            deprecate(
+                "prev_timestep",
+                "1.0.0",
+                "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
+            )
+        model_output_list = self.model_outputs
+
+        s0 = self.timestep_list[-1]
+        m0 = model_output_list[-1]
+        x = sample
+
+        if self.solver_p:
+            x_t = self.solver_p.step(model_output, s0, x).prev_sample
+            return x_t
+
+        sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[
+            self.step_index]  # pyright: ignore
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
+        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
+
+        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
+        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
+
+        h = lambda_t - lambda_s0
+        device = sample.device
+
+        rks = []
+        D1s = []
+        for i in range(1, order):
+            si = self.step_index - i  # pyright: ignore
+            mi = model_output_list[-(i + 1)]
+            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
+            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
+            rk = (lambda_si - lambda_s0) / h
+            rks.append(rk)
+            D1s.append((mi - m0) / rk)  # pyright: ignore
+
+        rks.append(1.0)
+        rks = torch.tensor(rks, device=device)
+
+        R = []
+        b = []
+
+        hh = -h if self.predict_x0 else h
+        h_phi_1 = torch.expm1(hh)  # h\phi_1(h) = e^h - 1
+        h_phi_k = h_phi_1 / hh - 1
+
+        factorial_i = 1
+
+        if self.config.solver_type == "bh1":
+            B_h = hh
+        elif self.config.solver_type == "bh2":
+            B_h = torch.expm1(hh)
+        else:
+            raise NotImplementedError()
+
+        for i in range(1, order + 1):
+            R.append(torch.pow(rks, i - 1))
+            b.append(h_phi_k * factorial_i / B_h)
+            factorial_i *= i + 1
+            h_phi_k = h_phi_k / hh - 1 / factorial_i
+
+        R = torch.stack(R)
+        b = torch.tensor(b, device=device)
+
+        if len(D1s) > 0:
+            D1s = torch.stack(D1s, dim=1)  # (B, K)
+            # for order 2, we use a simplified version
+            if order == 2:
+                rhos_p = torch.tensor([0.5], dtype=x.dtype, device=device)
+            else:
+                rhos_p = torch.linalg.solve(R[:-1, :-1],
+                                            b[:-1]).to(device).to(x.dtype)
+        else:
+            D1s = None
+
+        if self.predict_x0:
+            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
+            if D1s is not None:
+                pred_res = torch.einsum("k,bkc...->bc...", rhos_p,
+                                        D1s)  # pyright: ignore
+            else:
+                pred_res = 0
+            x_t = x_t_ - alpha_t * B_h * pred_res
+        else:
+            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
+            if D1s is not None:
+                pred_res = torch.einsum("k,bkc...->bc...", rhos_p,
+                                        D1s)  # pyright: ignore
+            else:
+                pred_res = 0
+            x_t = x_t_ - sigma_t * B_h * pred_res
+
+        x_t = x_t.to(x.dtype)
+        return x_t
+
+    def multistep_uni_c_bh_update(
+        self,
+        this_model_output: torch.Tensor,
+        *args,
+        last_sample: torch.Tensor = None,
+        this_sample: torch.Tensor = None,
+        order: int = None,  # pyright: ignore
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        One step for the UniC (B(h) version).
+
+        Args:
+            this_model_output (`torch.Tensor`):
+                The model outputs at `x_t`.
+            this_timestep (`int`):
+                The current timestep `t`.
+            last_sample (`torch.Tensor`):
+                The generated sample before the last predictor `x_{t-1}`.
+            this_sample (`torch.Tensor`):
+                The generated sample after the last predictor `x_{t}`.
+            order (`int`):
+                The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.
+
+        Returns:
+            `torch.Tensor`:
+                The corrected sample tensor at the current timestep.
+        """
+        this_timestep = args[0] if len(args) > 0 else kwargs.pop(
+            "this_timestep", None)
+        if last_sample is None:
+            if len(args) > 1:
+                last_sample = args[1]
+            else:
+                raise ValueError(
+                    " missing`last_sample` as a required keyward argument")
+        if this_sample is None:
+            if len(args) > 2:
+                this_sample = args[2]
+            else:
+                raise ValueError(
+                    " missing`this_sample` as a required keyward argument")
+        if order is None:
+            if len(args) > 3:
+                order = args[3]
+            else:
+                raise ValueError(
+                    " missing`order` as a required keyward argument")
+        if this_timestep is not None:
+            deprecate(
+                "this_timestep",
+                "1.0.0",
+                "Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
+            )
+
+        model_output_list = self.model_outputs
+
+        m0 = model_output_list[-1]
+        x = last_sample
+        x_t = this_sample
+        model_t = this_model_output
+
+        sigma_t, sigma_s0 = self.sigmas[self.step_index], self.sigmas[
+            self.step_index - 1]  # pyright: ignore
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
+        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
+
+        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
+        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
+
+        h = lambda_t - lambda_s0
+        device = this_sample.device
+
+        rks = []
+        D1s = []
+        for i in range(1, order):
+            si = self.step_index - (i + 1)  # pyright: ignore
+            mi = model_output_list[-(i + 1)]
+            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
+            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
+            rk = (lambda_si - lambda_s0) / h
+            rks.append(rk)
+            D1s.append((mi - m0) / rk)  # pyright: ignore
+
+        rks.append(1.0)
+        rks = torch.tensor(rks, device=device)
+
+        R = []
+        b = []
+
+        hh = -h if self.predict_x0 else h
+        h_phi_1 = torch.expm1(hh)  # h\phi_1(h) = e^h - 1
+        h_phi_k = h_phi_1 / hh - 1
+
+        factorial_i = 1
+
+        if self.config.solver_type == "bh1":
+            B_h = hh
+        elif self.config.solver_type == "bh2":
+            B_h = torch.expm1(hh)
+        else:
+            raise NotImplementedError()
+
+        for i in range(1, order + 1):
+            R.append(torch.pow(rks, i - 1))
+            b.append(h_phi_k * factorial_i / B_h)
+            factorial_i *= i + 1
+            h_phi_k = h_phi_k / hh - 1 / factorial_i
+
+        R = torch.stack(R)
+        b = torch.tensor(b, device=device)
+
+        if len(D1s) > 0:
+            D1s = torch.stack(D1s, dim=1)
+        else:
+            D1s = None
+
+        # for order 1, we use a simplified version
+        if order == 1:
+            rhos_c = torch.tensor([0.5], dtype=x.dtype, device=device)
+        else:
+            rhos_c = torch.linalg.solve(R, b).to(device).to(x.dtype)
+
+        if self.predict_x0:
+            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
+            if D1s is not None:
+                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
+            else:
+                corr_res = 0
+            D1_t = model_t - m0
+            x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
+        else:
+            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
+            if D1s is not None:
+                corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s)
+            else:
+                corr_res = 0
+            D1_t = model_t - m0
+            x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
+        x_t = x_t.to(x.dtype)
+        return x_t
+
+    def index_for_timestep(self, timestep, schedule_timesteps=None):
+        if schedule_timesteps is None:
+            schedule_timesteps = self.timesteps
+
+        indices = (schedule_timesteps == timestep).nonzero()
+
+        # The sigma index that is taken for the **very** first `step`
+        # is always the second index (or the last index if there is only 1)
+        # This way we can ensure we don't accidentally skip a sigma in
+        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
+        pos = 1 if len(indices) > 1 else 0
+
+        return indices[pos].item()
+
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
+    def _init_step_index(self, timestep):
+        """
+        Initialize the step_index counter for the scheduler.
+        """
+
+        if self.begin_index is None:
+            if isinstance(timestep, torch.Tensor):
+                timestep = timestep.to(self.timesteps.device)
+            self._step_index = self.index_for_timestep(timestep)
+        else:
+            self._step_index = self._begin_index
+
+    def step(self,
+             model_output: torch.Tensor,
+             timestep: Union[int, torch.Tensor],
+             sample: torch.Tensor,
+             return_dict: bool = True,
+             generator=None) -> Union[SchedulerOutput, Tuple]:
+        """
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the multistep UniPC.
+
+        Args:
+            model_output (`torch.Tensor`):
+                The direct output from learned diffusion model.
+            timestep (`int`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by the diffusion process.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
+
+        Returns:
+            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
+
+        """
+        if self.num_inference_steps is None:
+            raise ValueError(
+                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
+            )
+
+        if self.step_index is None:
+            self._init_step_index(timestep)
+
+        use_corrector = (
+            self.step_index > 0 and
+            self.step_index - 1 not in self.disable_corrector and
+            self.last_sample is not None  # pyright: ignore
+        )
+
+        model_output_convert = self.convert_model_output(
+            model_output, sample=sample)
+        if use_corrector:
+            sample = self.multistep_uni_c_bh_update(
+                this_model_output=model_output_convert,
+                last_sample=self.last_sample,
+                this_sample=sample,
+                order=self.this_order,
+            )
+
+        for i in range(self.config.solver_order - 1):
+            self.model_outputs[i] = self.model_outputs[i + 1]
+            self.timestep_list[i] = self.timestep_list[i + 1]
+
+        self.model_outputs[-1] = model_output_convert
+        self.timestep_list[-1] = timestep  # pyright: ignore
+
+        if self.config.lower_order_final:
+            this_order = min(self.config.solver_order,
+                             len(self.timesteps) -
+                             self.step_index)  # pyright: ignore
+        else:
+            this_order = self.config.solver_order
+
+        self.this_order = min(this_order,
+                              self.lower_order_nums + 1)  # warmup for multistep
+        assert self.this_order > 0
+
+        self.last_sample = sample
+        prev_sample = self.multistep_uni_p_bh_update(
+            model_output=model_output,  # pass the original non-converted model output, in case solver-p is used
+            sample=sample,
+            order=self.this_order,
+        )
+
+        if self.lower_order_nums < self.config.solver_order:
+            self.lower_order_nums += 1
+
+        # upon completion increase step index by one
+        self._step_index += 1  # pyright: ignore
+
+        if not return_dict:
+            return (prev_sample,)
+
+        return SchedulerOutput(prev_sample=prev_sample)
+
+    def scale_model_input(self, sample: torch.Tensor, *args,
+                          **kwargs) -> torch.Tensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.Tensor`):
+                The input sample.
+
+        Returns:
+            `torch.Tensor`:
+                A scaled input sample.
+        """
+        return sample
+
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
+    def add_noise(
+        self,
+        original_samples: torch.Tensor,
+        noise: torch.Tensor,
+        timesteps: torch.IntTensor,
+    ) -> torch.Tensor:
+        # Make sure sigmas and timesteps have the same device and dtype as original_samples
+        sigmas = self.sigmas.to(
+            device=original_samples.device, dtype=original_samples.dtype)
+        if original_samples.device.type == "mps" and torch.is_floating_point(
+                timesteps):
+            # mps does not support float64
+            schedule_timesteps = self.timesteps.to(
+                original_samples.device, dtype=torch.float32)
+            timesteps = timesteps.to(
+                original_samples.device, dtype=torch.float32)
+        else:
+            schedule_timesteps = self.timesteps.to(original_samples.device)
+            timesteps = timesteps.to(original_samples.device)
+
+        # begin_index is None when the scheduler is used for training or pipeline does not implement set_begin_index
+        if self.begin_index is None:
+            step_indices = [
+                self.index_for_timestep(t, schedule_timesteps)
+                for t in timesteps
+            ]
+        elif self.step_index is not None:
+            # add_noise is called after first denoising step (for inpainting)
+            step_indices = [self.step_index] * timesteps.shape[0]
+        else:
+            # add noise is called before first denoising step to create initial latent(img2img)
+            step_indices = [self.begin_index] * timesteps.shape[0]
+
+        sigma = sigmas[step_indices].flatten()
+        while len(sigma.shape) < len(original_samples.shape):
+            sigma = sigma.unsqueeze(-1)
+
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
+        return noisy_samples
+
+    def __len__(self):
+        return self.config.num_train_timesteps