# 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 ..configuration_utils import ConfigMixin, register_to_config from ..utils import deprecate from ..utils.torch_utils import randn_tensor from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput # 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`) 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`, `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_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)`. 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, use_karras_sigmas: Optional[bool] = False, use_lu_lambdas: Optional[bool] = False, final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min" lambda_min_clipped: float = -float("inf"), variance_type: Optional[str] = None, timestep_spacing: str = "linspace", steps_offset: int = 0, rescale_betas_zero_snr: bool = False, ): 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__}") if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) if rescale_betas_zero_snr: # Close to 0 without being 0 so first sigma is not inf # FP16 smallest positive subnormal works well here self.alphas_cumprod[-1] = 2**-24 # 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, ): """ 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. timesteps (`List[int]`, *optional*): Custom timesteps used to support arbitrary timesteps schedule. If `None`, timesteps will be generated based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` and `sigmas` must be `None`, and `timestep_spacing` attribute will be ignored. """ if num_inference_steps is None and timesteps is None: raise ValueError("Must pass exactly one of `num_inference_steps` or `timesteps`.") if num_inference_steps is not None and timesteps is not None: raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.") if timesteps is not None and self.config.use_karras_sigmas: raise ValueError("Cannot use `timesteps` with `config.use_karras_sigmas = True`") if timesteps is not None and self.config.use_lu_lambdas: raise ValueError("Cannot use `timesteps` with `config.use_lu_lambdas = True`") if timesteps is not None: timesteps = np.array(timesteps).astype(np.int64) else: # 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) last_timestep = ((self.config.num_train_timesteps - clipped_idx).numpy()).item() # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891 if self.config.timestep_spacing == "linspace": timesteps = ( np.linspace(0, last_timestep - 1, num_inference_steps + 1) .round()[::-1][:-1] .copy() .astype(np.int64) ) elif self.config.timestep_spacing == "leading": step_ratio = last_timestep // (num_inference_steps + 1) # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = ( (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64) ) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / num_inference_steps # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = np.arange(last_timestep, 0, -step_ratio).round().copy().astype(np.int64) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'." ) sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) log_sigmas = np.log(sigmas) if self.config.use_karras_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() elif self.config.use_lu_lambdas: lambdas = np.flip(log_sigmas.copy()) lambdas = self._convert_to_lu(in_lambdas=lambdas, num_inference_steps=num_inference_steps) sigmas = np.exp(lambdas) 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 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}" ) sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32) self.sigmas = torch.from_numpy(sigmas) self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64) self.num_inference_steps = len(timesteps) self.model_outputs = [ None, ] * self.config.solver_order self.lower_order_nums = 0 # 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**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.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 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 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: 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, **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 ) 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: int, 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) 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