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diff --git a/schedulers/scheduling_deis_multistep.py b/schedulers/scheduling_deis_multistep.py
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-# Copyright 2022 FLAIR Lab 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: check https://arxiv.org/abs/2204.13902 and https://github.com/qsh-zh/deis for more info
-# The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
-
-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
-
-
-def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
-    """
-    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.
-
-    Returns:
-        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
-    """
-
-    def alpha_bar(time_step):
-        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
-
-    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(t2) / alpha_bar(t1), max_beta))
-    return torch.tensor(betas, dtype=torch.float32)
-
-
-class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
-    """
-    DEIS (https://arxiv.org/abs/2204.13902) is a fast high order solver for diffusion ODEs. We slightly modify the
-    polynomial fitting formula in log-rho space instead of the original linear t space in DEIS paper. The modification
-    enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver. More
-    variants of DEIS can be found in https://github.com/qsh-zh/deis.
-
-    Currently, we support the log-rho multistep DEIS. We recommend to use `solver_order=2 / 3` while `solver_order=1`
-    reduces to DDIM.
-
-    We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space
-    diffusion models, you can set `thresholding=True` to use the dynamic thresholding.
-
-    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
-    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
-    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
-    [`~SchedulerMixin.from_pretrained`] functions.
-
-    Args:
-        num_train_timesteps (`int`): number of diffusion steps used to train the model.
-        beta_start (`float`): the starting `beta` value of inference.
-        beta_end (`float`): the final `beta` value.
-        beta_schedule (`str`):
-            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):
-            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        solver_order (`int`, default `2`):
-            the order of DEIS; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and
-            `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, default `epsilon`):
-            indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`,
-            or `v-prediction`.
-        thresholding (`bool`, default `False`):
-            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
-            Note that the thresholding method is unsuitable for latent-space diffusion models (such as
-            stable-diffusion).
-        dynamic_thresholding_ratio (`float`, default `0.995`):
-            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
-            (https://arxiv.org/abs/2205.11487).
-        sample_max_value (`float`, default `1.0`):
-            the threshold value for dynamic thresholding. Valid woks when `thresholding=True`
-        algorithm_type (`str`, default `deis`):
-            the algorithm type for the solver. current we support multistep deis, we will add other variants of DEIS in
-            the future
-        lower_order_final (`bool`, default `True`):
-            whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically
-            find this trick can stabilize the sampling of DEIS for steps < 15, especially for steps <= 10.
-
-    """
-
-    _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[np.ndarray] = 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 = "deis",
-        solver_type: str = "logrho",
-        lower_order_final: bool = True,
-    ):
-        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} does 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)
-
-        # standard deviation of the initial noise distribution
-        self.init_noise_sigma = 1.0
-
-        # settings for DEIS
-        if algorithm_type not in ["deis"]:
-            if algorithm_type in ["dpmsolver", "dpmsolver++"]:
-                algorithm_type = "deis"
-            else:
-                raise NotImplementedError(f"{algorithm_type} does is not implemented for {self.__class__}")
-
-        if solver_type not in ["logrho"]:
-            if solver_type in ["midpoint", "heun"]:
-                solver_type = "logrho"
-            else:
-                raise NotImplementedError(f"solver type {solver_type} does is not implemented for {self.__class__}")
-
-        # 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
-
-    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
-        """
-        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
-
-        Args:
-            num_inference_steps (`int`):
-                the number of diffusion steps used when generating samples with a pre-trained model.
-            device (`str` or `torch.device`, optional):
-                the device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
-        """
-        self.num_inference_steps = num_inference_steps
-        timesteps = (
-            np.linspace(0, self.num_train_timesteps - 1, num_inference_steps + 1)
-            .round()[::-1][:-1]
-            .copy()
-            .astype(np.int64)
-        )
-        self.timesteps = torch.from_numpy(timesteps).to(device)
-        self.model_outputs = [
-            None,
-        ] * self.config.solver_order
-        self.lower_order_nums = 0
-
-    def convert_model_output(
-        self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
-    ) -> torch.FloatTensor:
-        """
-        Convert the model output to the corresponding type that the algorithm DEIS needs.
-
-        Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-
-        Returns:
-            `torch.FloatTensor`: the converted model output.
-        """
-        if self.config.prediction_type == "epsilon":
-            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
-            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":
-            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
-            x0_pred = alpha_t * sample - sigma_t * model_output
-        else:
-            raise ValueError(
-                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
-                " `v_prediction` for the DEISMultistepScheduler."
-            )
-
-        if self.config.thresholding:
-            # Dynamic thresholding in https://arxiv.org/abs/2205.11487
-            orig_dtype = x0_pred.dtype
-            if orig_dtype not in [torch.float, torch.double]:
-                x0_pred = x0_pred.float()
-            dynamic_max_val = torch.quantile(
-                torch.abs(x0_pred).reshape((x0_pred.shape[0], -1)), self.config.dynamic_thresholding_ratio, dim=1
-            )
-            dynamic_max_val = torch.maximum(
-                dynamic_max_val,
-                self.config.sample_max_value * torch.ones_like(dynamic_max_val).to(dynamic_max_val.device),
-            )[(...,) + (None,) * (x0_pred.ndim - 1)]
-            x0_pred = torch.clamp(x0_pred, -dynamic_max_val, dynamic_max_val) / dynamic_max_val
-            x0_pred = x0_pred.type(orig_dtype)
-
-        if self.config.algorithm_type == "deis":
-            alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
-            return (sample - alpha_t * x0_pred) / sigma_t
-        else:
-            raise NotImplementedError("only support log-rho multistep deis now")
-
-    def deis_first_order_update(
-        self,
-        model_output: torch.FloatTensor,
-        timestep: int,
-        prev_timestep: int,
-        sample: torch.FloatTensor,
-    ) -> torch.FloatTensor:
-        """
-        One step for the first-order DEIS (equivalent to DDIM).
-
-        Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
-            sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-
-        Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
-        """
-        lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
-        alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
-        sigma_t, _ = self.sigma_t[prev_timestep], self.sigma_t[timestep]
-        h = lambda_t - lambda_s
-        if self.config.algorithm_type == "deis":
-            x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
-        else:
-            raise NotImplementedError("only support log-rho multistep deis now")
-        return x_t
-
-    def multistep_deis_second_order_update(
-        self,
-        model_output_list: List[torch.FloatTensor],
-        timestep_list: List[int],
-        prev_timestep: int,
-        sample: torch.FloatTensor,
-    ) -> torch.FloatTensor:
-        """
-        One step for the second-order multistep DEIS.
-
-        Args:
-            model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
-            sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-
-        Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
-        """
-        t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
-        m0, m1 = model_output_list[-1], model_output_list[-2]
-        alpha_t, alpha_s0, alpha_s1 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1]
-        sigma_t, sigma_s0, sigma_s1 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1]
-
-        rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1
-
-        if self.config.algorithm_type == "deis":
-
-            def ind_fn(t, b, c):
-                # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
-                return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))
-
-            coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
-            coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)
-
-            x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1)
-            return x_t
-        else:
-            raise NotImplementedError("only support log-rho multistep deis now")
-
-    def multistep_deis_third_order_update(
-        self,
-        model_output_list: List[torch.FloatTensor],
-        timestep_list: List[int],
-        prev_timestep: int,
-        sample: torch.FloatTensor,
-    ) -> torch.FloatTensor:
-        """
-        One step for the third-order multistep DEIS.
-
-        Args:
-            model_output_list (`List[torch.FloatTensor]`):
-                direct outputs from learned diffusion model at current and latter timesteps.
-            timestep (`int`): current and latter discrete timestep in the diffusion chain.
-            prev_timestep (`int`): previous discrete timestep in the diffusion chain.
-            sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-
-        Returns:
-            `torch.FloatTensor`: the sample tensor at the previous timestep.
-        """
-        t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
-        m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
-        alpha_t, alpha_s0, alpha_s1, alpha_s2 = self.alpha_t[t], self.alpha_t[s0], self.alpha_t[s1], self.alpha_t[s2]
-        sigma_t, sigma_s0, sigma_s1, simga_s2 = self.sigma_t[t], self.sigma_t[s0], self.sigma_t[s1], self.sigma_t[s2]
-        rho_t, rho_s0, rho_s1, rho_s2 = (
-            sigma_t / alpha_t,
-            sigma_s0 / alpha_s0,
-            sigma_s1 / alpha_s1,
-            simga_s2 / alpha_s2,
-        )
-
-        if self.config.algorithm_type == "deis":
-
-            def ind_fn(t, b, c, d):
-                # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
-                numerator = t * (
-                    np.log(c) * (np.log(d) - np.log(t) + 1)
-                    - np.log(d) * np.log(t)
-                    + np.log(d)
-                    + np.log(t) ** 2
-                    - 2 * np.log(t)
-                    + 2
-                )
-                denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
-                return numerator / denominator
-
-            coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
-            coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
-            coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)
-
-            x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)
-
-            return x_t
-        else:
-            raise NotImplementedError("only support log-rho multistep deis now")
-
-    def step(
-        self,
-        model_output: torch.FloatTensor,
-        timestep: int,
-        sample: torch.FloatTensor,
-        return_dict: bool = True,
-    ) -> Union[SchedulerOutput, Tuple]:
-        """
-        Step function propagating the sample with the multistep DEIS.
-
-        Args:
-            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
-            sample (`torch.FloatTensor`):
-                current instance of sample being created by diffusion process.
-            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
-
-        Returns:
-            [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is
-            True, otherwise a `tuple`. When returning a tuple, 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 isinstance(timestep, torch.Tensor):
-            timestep = timestep.to(self.timesteps.device)
-        step_index = (self.timesteps == timestep).nonzero()
-        if len(step_index) == 0:
-            step_index = len(self.timesteps) - 1
-        else:
-            step_index = step_index.item()
-        prev_timestep = 0 if step_index == len(self.timesteps) - 1 else self.timesteps[step_index + 1]
-        lower_order_final = (
-            (step_index == len(self.timesteps) - 1) and self.config.lower_order_final and len(self.timesteps) < 15
-        )
-        lower_order_second = (
-            (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, timestep, 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
-
-        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
-            prev_sample = self.deis_first_order_update(model_output, timestep, prev_timestep, sample)
-        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
-            timestep_list = [self.timesteps[step_index - 1], timestep]
-            prev_sample = self.multistep_deis_second_order_update(
-                self.model_outputs, timestep_list, prev_timestep, sample
-            )
-        else:
-            timestep_list = [self.timesteps[step_index - 2], self.timesteps[step_index - 1], timestep]
-            prev_sample = self.multistep_deis_third_order_update(
-                self.model_outputs, timestep_list, prev_timestep, sample
-            )
-
-        if self.lower_order_nums < self.config.solver_order:
-            self.lower_order_nums += 1
-
-        if not return_dict:
-            return (prev_sample,)
-
-        return SchedulerOutput(prev_sample=prev_sample)
-
-    def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor:
-        """
-        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
-        current timestep.
-
-        Args:
-            sample (`torch.FloatTensor`): input sample
-
-        Returns:
-            `torch.FloatTensor`: scaled input sample
-        """
-        return sample
-
-    def add_noise(
-        self,
-        original_samples: torch.FloatTensor,
-        noise: torch.FloatTensor,
-        timesteps: torch.IntTensor,
-    ) -> torch.FloatTensor:
-        # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
-        self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
-        timesteps = timesteps.to(original_samples.device)
-
-        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
-        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
-        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
-            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
-
-        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
-        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
-        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
-            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
-
-        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
-        return noisy_samples
-
-    def get_velocity(
-        self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor
-    ) -> torch.FloatTensor:
-        # Make sure alphas_cumprod and timestep have same device and dtype as sample
-        self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
-        timesteps = timesteps.to(sample.device)
-
-        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
-        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
-        while len(sqrt_alpha_prod.shape) < len(sample.shape):
-            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
-
-        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
-        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
-        while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
-            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
-
-        velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
-        return velocity
-
-    def __len__(self):
-        return self.config.num_train_timesteps