# Copyright 2023 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 ..configuration_utils import ConfigMixin, register_to_config from ..utils import deprecate, logging from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput logger = logging.get_logger(__name__) # pylint: disable=invalid-name # 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_tranform_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) class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin): """ `DPMSolverSinglestepScheduler` 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`) or `v_prediction` (see section 2.4 of [Imagen Video](https://imagen.research.google/video/paper.pdf) paper). 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` or `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. 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}. final_sigmas_type (`str`, *optional*, 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. """ _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 = "dpmsolver++", solver_type: str = "midpoint", lower_order_final: bool = True, use_karras_sigmas: Optional[bool] = False, final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min" lambda_min_clipped: float = -float("inf"), variance_type: Optional[str] = None, ): if algorithm_type == "dpmsolver": deprecation_message = "algorithm_type `dpmsolver` is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead" deprecate("algorithm_types=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} 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) 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++"]: if algorithm_type == "deis": self.register_to_config(algorithm_type="dpmsolver++") else: raise NotImplementedError(f"{algorithm_type} does 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} does is not implemented for {self.__class__}") if algorithm_type != "dpmsolver++" and final_sigmas_type == "zero": raise ValueError( f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please chooose `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.sample = None self.order_list = self.get_order_list(num_train_timesteps) self._step_index = None self.sigmas.to("cpu") # to avoid too much CPU/GPU communication def get_order_list(self, num_inference_steps: int) -> List[int]: """ Computes the solver order at each time step. Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. """ steps = num_inference_steps order = self.config.solver_order if self.config.lower_order_final: if order == 3: if steps % 3 == 0: orders = [1, 2, 3] * (steps // 3 - 1) + [1, 2] + [1] elif steps % 3 == 1: orders = [1, 2, 3] * (steps // 3) + [1] else: orders = [1, 2, 3] * (steps // 3) + [1, 2] elif order == 2: if steps % 2 == 0: orders = [1, 2] * (steps // 2) else: orders = [1, 2] * (steps // 2) + [1] elif order == 1: orders = [1] * steps else: if order == 3: orders = [1, 2, 3] * (steps // 3) elif order == 2: orders = [1, 2] * (steps // 2) elif order == 1: orders = [1] * steps return orders @property def step_index(self): """ The index counter for current timestep. It will increae 1 after each scheduler step. """ return self._step_index def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (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 # Clipping the minimum of all lambda(t) for numerical stability. # This is critical for cosine (squaredcos_cap_v2) noise schedule. clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped) timesteps = ( np.linspace(0, self.config.num_train_timesteps - 1 - clipped_idx, num_inference_steps + 1) .round()[::-1][:-1] .copy() .astype(np.int64) ) sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) if self.config.use_karras_sigmas: log_sigmas = np.log(sigmas) sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round() else: sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) 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 `sigma_min` or `zero`, but got {self.config.final_sigmas_type}" ) sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32) self.sigmas = torch.from_numpy(sigmas).to(device=device) self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64) self.model_outputs = [None] * self.config.solver_order self.sample = None if not self.config.lower_order_final and num_inference_steps % self.config.solver_order != 0: logger.warn( "Changing scheduler {self.config} to have `lower_order_final` set to True to handle uneven amount of inference steps. Please make sure to always use an even number of `num_inference steps when using `lower_order_final=True`." ) self.register_to_config(lower_order_final=True) if not self.config.lower_order_final and self.config.final_sigmas_type == "zero": logger.warn( " `last_sigmas_type='zero'` is not supported for `lower_order_final=False`. Changing scheduler {self.config} to have `lower_order_final` set to True." ) self.register_to_config(lower_order_final=True) self.order_list = self.get_order_list(num_inference_steps) # add an index counter for schedulers that allow duplicated timesteps self._step_index = None 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.FloatTensor) -> torch.FloatTensor: """ "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 # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t def _sigma_to_alpha_sigma_t(self, sigma): alpha_t = 1 / ((sigma**2 + 1) ** 0.5) sigma_t = sigma * alpha_t return alpha_t, sigma_t # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor: """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_model_output( self, model_output: torch.FloatTensor, *args, sample: torch.FloatTensor = None, **kwargs, ) -> torch.FloatTensor: """ 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. The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise prediction and data prediction models. Args: model_output (`torch.FloatTensor`): The direct output from the learned diffusion model. sample (`torch.FloatTensor`): A current instance of a sample created by the diffusion process. Returns: `torch.FloatTensor`: 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 == "dpmsolver++": if self.config.prediction_type == "epsilon": # DPM-Solver and DPM-Solver++ only need the "mean" output. if self.config.variance_type in ["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 else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction` for the DPMSolverSinglestepScheduler." ) 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 == "dpmsolver": if self.config.prediction_type == "epsilon": # DPM-Solver and DPM-Solver++ only need the "mean" output. if self.config.variance_type in ["learned_range"]: model_output = model_output[:, :3] return 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 return epsilon 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 return epsilon else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction` for the DPMSolverSinglestepScheduler." ) def dpm_solver_first_order_update( self, model_output: torch.FloatTensor, *args, sample: torch.FloatTensor = None, **kwargs, ) -> torch.FloatTensor: """ One step for the first-order DPMSolver (equivalent to DDIM). Args: model_output (`torch.FloatTensor`): The direct output from the learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): A current instance of a sample created by the diffusion process. Returns: `torch.FloatTensor`: 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 return x_t def singlestep_dpm_solver_second_order_update( self, model_output_list: List[torch.FloatTensor], *args, sample: torch.FloatTensor = None, **kwargs, ) -> torch.FloatTensor: """ One step for the second-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the time `timestep_list[-2]`. Args: model_output_list (`List[torch.FloatTensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): A current instance of a sample created by the diffusion process. Returns: `torch.FloatTensor`: 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_s1, lambda_s0 - lambda_s1 r0 = h_0 / h D0, D1 = m1, (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_s1) * 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_s1) * 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_s1) * 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_s1) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1 ) return x_t def singlestep_dpm_solver_third_order_update( self, model_output_list: List[torch.FloatTensor], *args, sample: torch.FloatTensor = None, **kwargs, ) -> torch.FloatTensor: """ One step for the third-order singlestep DPMSolver that computes the solution at time `prev_timestep` from the time `timestep_list[-3]`. Args: model_output_list (`List[torch.FloatTensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): A current instance of a sample created by diffusion process. Returns: `torch.FloatTensor`: 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_s2, lambda_s0 - lambda_s2, lambda_s1 - lambda_s2 r0, r1 = h_0 / h, h_1 / h D0 = m2 D1_0, D1_1 = (1.0 / r1) * (m1 - m2), (1.0 / r0) * (m0 - m2) D1 = (r0 * D1_0 - r1 * D1_1) / (r0 - r1) D2 = 2.0 * (D1_1 - D1_0) / (r0 - r1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s2) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * D0 + (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1_1 ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s2) * 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 if self.config.solver_type == "midpoint": x_t = ( (alpha_t / alpha_s2) * sample - (sigma_t * (torch.exp(h) - 1.0)) * D0 - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1_1 ) elif self.config.solver_type == "heun": x_t = ( (alpha_t / alpha_s2) * 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 ) return x_t def singlestep_dpm_solver_update( self, model_output_list: List[torch.FloatTensor], *args, sample: torch.FloatTensor = None, order: int = None, **kwargs, ) -> torch.FloatTensor: """ One step for the singlestep DPMSolver. Args: model_output_list (`List[torch.FloatTensor]`): The direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): The current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): A current instance of a sample created by diffusion process. order (`int`): The solver order at this step. Returns: `torch.FloatTensor`: 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 order is None: if len(args) > 3: order = args[3] else: raise ValueError(" missing `order` 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`", ) if order == 1: return self.dpm_solver_first_order_update(model_output_list[-1], sample=sample) elif order == 2: return self.singlestep_dpm_solver_second_order_update(model_output_list, sample=sample) elif order == 3: return self.singlestep_dpm_solver_third_order_update(model_output_list, sample=sample) else: raise ValueError(f"Order must be 1, 2, 3, got {order}") def _init_step_index(self, timestep): if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) index_candidates = (self.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() self._step_index = step_index def step( self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor, 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 singlestep DPMSolver. Args: model_output (`torch.FloatTensor`): The direct output from learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.FloatTensor`): 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) 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 order = self.order_list[self.step_index] # For img2img denoising might start with order>1 which is not possible # In this case make sure that the first two steps are both order=1 while self.model_outputs[-order] is None: order -= 1 # For single-step solvers, we use the initial value at each time with order = 1. if order == 1: self.sample = sample prev_sample = self.singlestep_dpm_solver_update(self.model_outputs, sample=self.sample, order=order) # 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.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`): The input sample. Returns: `torch.FloatTensor`: A scaled input sample. """ return sample # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise def add_noise( self, original_samples: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor, ) -> torch.FloatTensor: # 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) step_indices = [] for timestep in timesteps: index_candidates = (schedule_timesteps == timestep).nonzero() if len(index_candidates) == 0: step_index = len(schedule_timesteps) - 1 elif len(index_candidates) > 1: step_index = index_candidates[1].item() else: step_index = index_candidates[0].item() step_indices.append(step_index) 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