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extensions_built_in/diffusion_models/omnigen2/src/schedulers/scheduling_dpmsolver_multistep.py

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+# Copyright 2024 TSAIL Team and The HuggingFace Team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# DISCLAIMER: This file is strongly influenced by https://github.com/LuChengTHU/dpm-solver
+
+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.utils import deprecate, is_scipy_available
+from diffusers.utils.torch_utils import randn_tensor
+from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
+
+
+if is_scipy_available():
+    import scipy.stats
+
+
+# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
+def betas_for_alpha_bar(
+    num_diffusion_timesteps,
+    max_beta=0.999,
+    alpha_transform_type="cosine",
+):
+    """
+    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
+    (1-beta) over time from t = [0,1].
+
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
+                     prevent singularities.
+        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
+                     Choose from `cosine` or `exp`
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
+    """
+    if alpha_transform_type == "cosine":
+
+        def alpha_bar_fn(t):
+            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    elif alpha_transform_type == "exp":
+
+        def alpha_bar_fn(t):
+            return math.exp(t * -12.0)
+
+    else:
+        raise ValueError(f"Unsupported alpha_transform_type: {alpha_transform_type}")
+
+    betas = []
+    for i in range(num_diffusion_timesteps):
+        t1 = i / num_diffusion_timesteps
+        t2 = (i + 1) / num_diffusion_timesteps
+        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
+    return torch.tensor(betas, dtype=torch.float32)
+
+
+# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
+def rescale_zero_terminal_snr(betas):
+    """
+    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
+
+
+    Args:
+        betas (`torch.Tensor`):
+            the betas that the scheduler is being initialized with.
+
+    Returns:
+        `torch.Tensor`: rescaled betas with zero terminal SNR
+    """
+    # Convert betas to alphas_bar_sqrt
+    alphas = 1.0 - betas
+    alphas_cumprod = torch.cumprod(alphas, dim=0)
+    alphas_bar_sqrt = alphas_cumprod.sqrt()
+
+    # Store old values.
+    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
+    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
+
+    # Shift so the last timestep is zero.
+    alphas_bar_sqrt -= alphas_bar_sqrt_T
+
+    # Scale so the first timestep is back to the old value.
+    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
+
+    # Convert alphas_bar_sqrt to betas
+    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
+    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
+    alphas = torch.cat([alphas_bar[0:1], alphas])
+    betas = 1 - alphas
+
+    return betas
+
+
+class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
+    """
+    `DPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
+
+    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.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        solver_order (`int`, defaults to 2):
+            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
+            sampling, and `solver_order=3` for unconditional sampling.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample), `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper), or `flow_prediction`.
+        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
+            `algorithm_type="dpmsolver++"`.
+        algorithm_type (`str`, defaults to `dpmsolver++`):
+            Algorithm type for the solver; can be `dpmsolver`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
+            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
+            paper, and the `dpmsolver++` type implements the algorithms in the
+            [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to use `dpmsolver++` or
+            `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
+        solver_type (`str`, defaults to `midpoint`):
+            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
+            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
+        lower_order_final (`bool`, defaults to `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.
+        euler_at_final (`bool`, defaults to `False`):
+            Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail
+            richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference
+            steps, but sometimes may result in blurring.
+        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.
+        use_beta_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
+            Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
+        use_lu_lambdas (`bool`, *optional*, defaults to `False`):
+            Whether to use the uniform-logSNR for step sizes proposed by Lu's DPM-Solver in the noise schedule during
+            the sampling process. If `True`, the sigmas and time steps are determined according to a sequence of
+            `lambda(t)`.
+        use_flow_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use flow sigmas for step sizes in the noise schedule during the sampling process.
+        flow_shift (`float`, *optional*, defaults to 1.0):
+            The shift value for the timestep schedule for flow matching.
+        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.
+        lambda_min_clipped (`float`, defaults to `-inf`):
+            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
+            cosine (`squaredcos_cap_v2`) noise schedule.
+        variance_type (`str`, *optional*):
+            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
+            contains the predicted Gaussian variance.
+        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.
+        rescale_betas_zero_snr (`bool`, defaults to `False`):
+            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
+            dark samples instead of limiting it to samples with medium brightness. Loosely related to
+            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
+    """
+
+    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
+    order = 1
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.0001,
+        beta_end: float = 0.02,
+        beta_schedule: str = "linear",
+        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
+        solver_order: int = 2,
+        prediction_type: str = "epsilon",
+        thresholding: bool = False,
+        dynamic_thresholding_ratio: float = 0.995,
+        sample_max_value: float = 1.0,
+        algorithm_type: str = "dpmsolver++",
+        solver_type: str = "midpoint",
+        lower_order_final: bool = True,
+        euler_at_final: bool = False,
+        final_sigmas_type: str = 'zero',
+        dynamic_time_shift: bool = True
+    ):
+        if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
+            deprecation_message = f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
+            deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0", deprecation_message)
+
+        if trained_betas is not None:
+            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
+        elif beta_schedule == "linear":
+            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
+        elif beta_schedule == "scaled_linear":
+            # this schedule is very specific to the latent diffusion model.
+            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
+        elif beta_schedule == "squaredcos_cap_v2":
+            # Glide cosine schedule
+            self.betas = betas_for_alpha_bar(num_train_timesteps)
+        else:
+            raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
+
+        # Currently we only support VP-type noise schedule
+        self.alpha_t = torch.sqrt(self.alphas_cumprod)
+        self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
+        self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
+        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
+
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
+        # settings for DPM-Solver
+        if algorithm_type not in ["dpmsolver", "dpmsolver++", "sde-dpmsolver", "sde-dpmsolver++"]:
+            if algorithm_type == "deis":
+                self.register_to_config(algorithm_type="dpmsolver++")
+            else:
+                raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}")
+
+        if solver_type not in ["midpoint", "heun"]:
+            if solver_type in ["logrho", "bh1", "bh2"]:
+                self.register_to_config(solver_type="midpoint")
+            else:
+                raise NotImplementedError(f"{solver_type} is not implemented for {self.__class__}")
+
+        # if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"] and final_sigmas_type == "zero":
+        #     raise ValueError(
+        #         f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please choose `sigma_min` instead."
+        #     )
+
+        # setable values
+        self.num_inference_steps = None
+        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
+        self.timesteps = torch.from_numpy(timesteps)
+        self.model_outputs = [None] * solver_order
+        self.lower_order_nums = 0
+        self._step_index = None
+        self._begin_index = None
+        self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
+
+    @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
+
+    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
+
+    def set_timesteps(
+        self,
+        num_inference_steps: int = None,
+        device: Union[str, torch.device] = None,
+        timesteps: Optional[List[int]] = None,
+        num_tokens: Optional[int] = None
+    ):
+        if timesteps is None:
+            self.num_inference_steps = num_inference_steps
+            timesteps = np.linspace(0, 1, num_inference_steps + 1, dtype=np.float32)[:-1]
+            if self.config.dynamic_time_shift and num_tokens is not None:
+                m = np.sqrt(num_tokens) / 40 # when input resolution is 320 * 320, m = 1, when input resolution is 1024 * 1024, m = 3.2
+                timesteps = timesteps / (m - m * timesteps + timesteps)
+
+        timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32, device=device)
+        sigmas = torch.cat([1 - timesteps, torch.zeros(1, device=timesteps.device)])
+
+        self.sigmas = sigmas
+        self.timesteps = timesteps
+
+        self.num_inference_steps = len(timesteps)
+
+        self.model_outputs = [
+            None,
+        ] * self.config.solver_order
+        self.lower_order_nums = 0
+
+        # 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_euler_discrete.EulerDiscreteScheduler._sigma_to_t
+    def _sigma_to_t(self, sigma, log_sigmas):
+        # get log sigma
+        log_sigma = np.log(np.maximum(sigma, 1e-10))
+
+        # get distribution
+        dists = log_sigma - log_sigmas[:, np.newaxis]
+
+        # get sigmas range
+        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
+        high_idx = low_idx + 1
+
+        low = log_sigmas[low_idx]
+        high = log_sigmas[high_idx]
+
+        # interpolate sigmas
+        w = (low - log_sigma) / (low - high)
+        w = np.clip(w, 0, 1)
+
+        # transform interpolation to time range
+        t = (1 - w) * low_idx + w * high_idx
+        t = t.reshape(sigma.shape)
+        return t
+
+    def _sigma_to_alpha_sigma_t(self, sigma):
+        alpha_t = 1 - sigma
+        sigma_t = sigma
+
+        return alpha_t, sigma_t
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
+    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
+        """Constructs the noise schedule of Karras et al. (2022)."""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        rho = 7.0  # 7.0 is the value used in the paper
+        ramp = np.linspace(0, 1, num_inference_steps)
+        min_inv_rho = sigma_min ** (1 / rho)
+        max_inv_rho = sigma_max ** (1 / rho)
+        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
+        return sigmas
+
+    def _convert_to_lu(self, in_lambdas: torch.Tensor, num_inference_steps) -> torch.Tensor:
+        """Constructs the noise schedule of Lu et al. (2022)."""
+
+        lambda_min: float = in_lambdas[-1].item()
+        lambda_max: float = in_lambdas[0].item()
+
+        rho = 1.0  # 1.0 is the value used in the paper
+        ramp = np.linspace(0, 1, num_inference_steps)
+        min_inv_rho = lambda_min ** (1 / rho)
+        max_inv_rho = lambda_max ** (1 / rho)
+        lambdas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
+        return lambdas
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
+    def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
+        """Constructs an exponential noise schedule."""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps))
+        return sigmas
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
+    def _convert_to_beta(
+        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
+    ) -> torch.Tensor:
+        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = np.array(
+            [
+                sigma_min + (ppf * (sigma_max - sigma_min))
+                for ppf in [
+                    scipy.stats.beta.ppf(timestep, alpha, beta)
+                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
+                ]
+            ]
+        )
+        return sigmas
+
+    def convert_model_output(
+        self,
+        model_output: torch.Tensor,
+        *args,
+        sample: torch.Tensor = None,
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
+        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
+        integral of the data prediction model.
+
+        <Tip>
+
+        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
+        prediction and data prediction models.
+
+        </Tip>
+
+        Args:
+            model_output (`torch.Tensor`):
+                The direct output from the learned diffusion model.
+            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`",
+            )
+
+        # DPM-Solver++ needs to solve an integral of the data prediction model.
+        if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
+            if self.config.prediction_type == "epsilon":
+                # DPM-Solver and DPM-Solver++ only need the "mean" output.
+                if self.config.variance_type in ["learned", "learned_range"]:
+                    model_output = model_output[:, :3]
+                sigma = self.sigmas[self.step_index]
+                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+                x0_pred = (sample - sigma_t * model_output) / alpha_t
+            elif self.config.prediction_type == "sample":
+                x0_pred = model_output
+            elif self.config.prediction_type == "v_prediction":
+                sigma = self.sigmas[self.step_index]
+                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+                x0_pred = alpha_t * sample - sigma_t * model_output
+            elif 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 DPMSolverMultistepScheduler."
+                )
+
+            if self.config.thresholding:
+                x0_pred = self._threshold_sample(x0_pred)
+
+            return x0_pred
+
+        # DPM-Solver needs to solve an integral of the noise prediction model.
+        elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
+            if self.config.prediction_type == "epsilon":
+                # DPM-Solver and DPM-Solver++ only need the "mean" output.
+                if self.config.variance_type in ["learned", "learned_range"]:
+                    epsilon = model_output[:, :3]
+                else:
+                    epsilon = model_output
+            elif self.config.prediction_type == "sample":
+                sigma = self.sigmas[self.step_index]
+                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+                epsilon = (sample - alpha_t * model_output) / sigma_t
+            elif self.config.prediction_type == "v_prediction":
+                sigma = self.sigmas[self.step_index]
+                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+                epsilon = alpha_t * model_output + sigma_t * sample
+            else:
+                raise ValueError(
+                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
+                    " `v_prediction` for the DPMSolverMultistepScheduler."
+                )
+
+            if self.config.thresholding:
+                sigma = self.sigmas[self.step_index]
+                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+                x0_pred = (sample - sigma_t * epsilon) / alpha_t
+                x0_pred = self._threshold_sample(x0_pred)
+                epsilon = (sample - alpha_t * x0_pred) / sigma_t
+
+            return epsilon
+
+    def dpm_solver_first_order_update(
+        self,
+        model_output: torch.Tensor,
+        *args,
+        sample: torch.Tensor = None,
+        noise: Optional[torch.Tensor] = None,
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        One step for the first-order DPMSolver (equivalent to DDIM).
+
+        Args:
+            model_output (`torch.Tensor`):
+                The direct output from the learned diffusion model.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by the diffusion process.
+
+        Returns:
+            `torch.Tensor`:
+                The sample tensor at the previous timestep.
+        """
+        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
+        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
+        if sample is None:
+            if len(args) > 2:
+                sample = args[2]
+            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`",
+            )
+
+        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`",
+            )
+
+        sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
+        alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
+        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
+        lambda_s = torch.log(alpha_s) - torch.log(sigma_s)
+
+        h = lambda_t - lambda_s
+        if self.config.algorithm_type == "dpmsolver++":
+            x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output
+        elif self.config.algorithm_type == "dpmsolver":
+            x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
+        elif self.config.algorithm_type == "sde-dpmsolver++":
+            assert noise is not None
+            x_t = (
+                (sigma_t / sigma_s * torch.exp(-h)) * sample
+                + (alpha_t * (1 - torch.exp(-2.0 * h))) * model_output
+                + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+            )
+        elif self.config.algorithm_type == "sde-dpmsolver":
+            assert noise is not None
+            x_t = (
+                (alpha_t / alpha_s) * sample
+                - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * model_output
+                + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
+            )
+        return x_t
+
+    def multistep_dpm_solver_second_order_update(
+        self,
+        model_output_list: List[torch.Tensor],
+        *args,
+        sample: torch.Tensor = None,
+        noise: Optional[torch.Tensor] = None,
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        One step for the second-order multistep DPMSolver.
+
+        Args:
+            model_output_list (`List[torch.Tensor]`):
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by the diffusion process.
+
+        Returns:
+            `torch.Tensor`:
+                The sample tensor at the previous timestep.
+        """
+        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
+        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
+        if sample is None:
+            if len(args) > 2:
+                sample = args[2]
+            else:
+                raise ValueError(" missing `sample` as a required keyward argument")
+        if timestep_list is not None:
+            deprecate(
+                "timestep_list",
+                "1.0.0",
+                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
+            )
+
+        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`",
+            )
+
+        sigma_t, sigma_s0, sigma_s1 = (
+            self.sigmas[self.step_index + 1],
+            self.sigmas[self.step_index],
+            self.sigmas[self.step_index - 1],
+        )
+
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
+        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
+        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
+
+        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
+        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
+        lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)
+
+        m0, m1 = model_output_list[-1], model_output_list[-2]
+
+        h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1
+        r0 = h_0 / h
+        D0, D1 = m0, (1.0 / r0) * (m0 - m1)
+        if self.config.algorithm_type == "dpmsolver++":
+            # See https://arxiv.org/abs/2211.01095 for detailed derivations
+            if self.config.solver_type == "midpoint":
+                x_t = (
+                    (sigma_t / sigma_s0) * sample
+                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
+                    - 0.5 * (alpha_t * (torch.exp(-h) - 1.0)) * D1
+                )
+            elif self.config.solver_type == "heun":
+                x_t = (
+                    (sigma_t / sigma_s0) * sample
+                    - (alpha_t * (torch.exp(-h) - 1.0)) * D0
+                    + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
+                )
+        elif self.config.algorithm_type == "dpmsolver":
+            # See https://arxiv.org/abs/2206.00927 for detailed derivations
+            if self.config.solver_type == "midpoint":
+                x_t = (
+                    (alpha_t / alpha_s0) * sample
+                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
+                    - 0.5 * (sigma_t * (torch.exp(h) - 1.0)) * D1
+                )
+            elif self.config.solver_type == "heun":
+                x_t = (
+                    (alpha_t / alpha_s0) * sample
+                    - (sigma_t * (torch.exp(h) - 1.0)) * D0
+                    - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
+                )
+        elif self.config.algorithm_type == "sde-dpmsolver++":
+            assert noise is not None
+            if self.config.solver_type == "midpoint":
+                x_t = (
+                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
+                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
+                    + 0.5 * (alpha_t * (1 - torch.exp(-2.0 * h))) * D1
+                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+                )
+            elif self.config.solver_type == "heun":
+                x_t = (
+                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
+                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
+                    + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1
+                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+                )
+        elif self.config.algorithm_type == "sde-dpmsolver":
+            assert noise is not None
+            if self.config.solver_type == "midpoint":
+                x_t = (
+                    (alpha_t / alpha_s0) * sample
+                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
+                    - (sigma_t * (torch.exp(h) - 1.0)) * D1
+                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
+                )
+            elif self.config.solver_type == "heun":
+                x_t = (
+                    (alpha_t / alpha_s0) * sample
+                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
+                    - 2.0 * (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
+                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
+                )
+        return x_t
+
+    def multistep_dpm_solver_third_order_update(
+        self,
+        model_output_list: List[torch.Tensor],
+        *args,
+        sample: torch.Tensor = None,
+        noise: Optional[torch.Tensor] = None,
+        **kwargs,
+    ) -> torch.Tensor:
+        """
+        One step for the third-order multistep DPMSolver.
+
+        Args:
+            model_output_list (`List[torch.Tensor]`):
+                The direct outputs from learned diffusion model at current and latter timesteps.
+            sample (`torch.Tensor`):
+                A current instance of a sample created by diffusion process.
+
+        Returns:
+            `torch.Tensor`:
+                The sample tensor at the previous timestep.
+        """
+
+        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
+        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
+        if sample is None:
+            if len(args) > 2:
+                sample = args[2]
+            else:
+                raise ValueError(" missing`sample` as a required keyward argument")
+        if timestep_list is not None:
+            deprecate(
+                "timestep_list",
+                "1.0.0",
+                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
+            )
+
+        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`",
+            )
+
+        sigma_t, sigma_s0, sigma_s1, sigma_s2 = (
+            self.sigmas[self.step_index + 1],
+            self.sigmas[self.step_index],
+            self.sigmas[self.step_index - 1],
+            self.sigmas[self.step_index - 2],
+        )
+
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
+        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
+        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
+        alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)
+
+        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
+        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
+        lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)
+        lambda_s2 = torch.log(alpha_s2) - torch.log(sigma_s2)
+
+        m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
+
+        h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2
+        r0, r1 = h_0 / h, h_1 / h
+        D0 = m0
+        D1_0, D1_1 = (1.0 / r0) * (m0 - m1), (1.0 / r1) * (m1 - m2)
+        D1 = D1_0 + (r0 / (r0 + r1)) * (D1_0 - D1_1)
+        D2 = (1.0 / (r0 + r1)) * (D1_0 - D1_1)
+        if self.config.algorithm_type == "dpmsolver++":
+            # See https://arxiv.org/abs/2206.00927 for detailed derivations
+            x_t = (
+                (sigma_t / sigma_s0) * sample
+                - (alpha_t * (torch.exp(-h) - 1.0)) * D0
+                + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
+                - (alpha_t * ((torch.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2
+            )
+        elif self.config.algorithm_type == "dpmsolver":
+            # See https://arxiv.org/abs/2206.00927 for detailed derivations
+            x_t = (
+                (alpha_t / alpha_s0) * sample
+                - (sigma_t * (torch.exp(h) - 1.0)) * D0
+                - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
+                - (sigma_t * ((torch.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2
+            )
+        elif self.config.algorithm_type == "sde-dpmsolver++":
+            assert noise is not None
+            x_t = (
+                (sigma_t / sigma_s0 * torch.exp(-h)) * sample
+                + (alpha_t * (1.0 - torch.exp(-2.0 * h))) * D0
+                + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1
+                + (alpha_t * ((1.0 - torch.exp(-2.0 * h) - 2.0 * h) / (2.0 * h) ** 2 - 0.5)) * D2
+                + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+            )
+        return x_t
+
+    def index_for_timestep(self, timestep, schedule_timesteps=None):
+        if schedule_timesteps is None:
+            schedule_timesteps = self.timesteps
+
+        index_candidates = (schedule_timesteps == timestep).nonzero()
+
+        if len(index_candidates) == 0:
+            step_index = len(self.timesteps) - 1
+        # 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)
+        elif len(index_candidates) > 1:
+            step_index = index_candidates[1].item()
+        else:
+            step_index = index_candidates[0].item()
+
+        return 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,
+        generator=None,
+        variance_noise: Optional[torch.Tensor] = None,
+        return_dict: bool = True,
+    ) -> Union[SchedulerOutput, Tuple]:
+        """
+        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
+        the multistep DPMSolver.
+
+        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.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            variance_noise (`torch.Tensor`):
+                Alternative to generating noise with `generator` by directly providing the noise for the variance
+                itself. Useful for methods such as [`LEdits++`].
+            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)
+
+        # Improve numerical stability for small number of steps
+        lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
+            self.config.euler_at_final
+            or (self.config.lower_order_final and len(self.timesteps) < 15)
+            or self.config.final_sigmas_type == "zero"
+        )
+        lower_order_second = (
+            (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
+        )
+
+        model_output = self.convert_model_output(model_output, sample=sample)
+        for i in range(self.config.solver_order - 1):
+            self.model_outputs[i] = self.model_outputs[i + 1]
+        self.model_outputs[-1] = model_output
+
+        # Upcast to avoid precision issues when computing prev_sample
+        sample = sample.to(torch.float32)
+        if self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"] and variance_noise is None:
+            noise = randn_tensor(
+                model_output.shape, generator=generator, device=model_output.device, dtype=torch.float32
+            )
+        elif self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
+            noise = variance_noise.to(device=model_output.device, dtype=torch.float32)
+        else:
+            noise = None
+
+        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
+            prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise)
+        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
+            prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise)
+        else:
+            prev_sample = self.multistep_dpm_solver_third_order_update(self.model_outputs, sample=sample, noise=noise)
+
+        if self.lower_order_nums < self.config.solver_order:
+            self.lower_order_nums += 1
+
+        # Cast sample back to expected dtype
+        prev_sample = prev_sample.to(model_output.dtype)
+
+        # upon completion increase step index by one
+        self._step_index += 1
+
+        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
+
+    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