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| # Copyright 2022 Katherine Crowson 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. | |
| import warnings | |
| from dataclasses import dataclass | |
| from typing import List, Optional, Tuple, Union | |
| import numpy as np | |
| import torch | |
| from scipy import integrate | |
| from ..configuration_utils import ConfigMixin, register_to_config | |
| from ..utils import _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS, BaseOutput | |
| from .scheduling_utils import SchedulerMixin | |
| # Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete | |
| class LMSDiscreteSchedulerOutput(BaseOutput): | |
| """ | |
| Output class for the scheduler's step function output. | |
| Args: | |
| prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): | |
| Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the | |
| denoising loop. | |
| pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): | |
| The predicted denoised sample (x_{0}) based on the model output from the current timestep. | |
| `pred_original_sample` can be used to preview progress or for guidance. | |
| """ | |
| prev_sample: torch.FloatTensor | |
| pred_original_sample: Optional[torch.FloatTensor] = None | |
| class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin): | |
| """ | |
| Linear Multistep Scheduler for discrete beta schedules. Based on the original k-diffusion implementation by | |
| Katherine Crowson: | |
| https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L181 | |
| [`~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` or `scaled_linear`. | |
| trained_betas (`np.ndarray`, optional): | |
| option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. | |
| prediction_type (`str`, default `epsilon`, optional): | |
| prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion | |
| process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4 | |
| https://imagen.research.google/video/paper.pdf) | |
| """ | |
| _compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy() | |
| order = 1 | |
| 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, | |
| prediction_type: str = "epsilon", | |
| ): | |
| 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 | |
| ) | |
| 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) | |
| sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
| sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32) | |
| self.sigmas = torch.from_numpy(sigmas) | |
| # standard deviation of the initial noise distribution | |
| self.init_noise_sigma = self.sigmas.max() | |
| # setable values | |
| self.num_inference_steps = None | |
| timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy() | |
| self.timesteps = torch.from_numpy(timesteps) | |
| self.derivatives = [] | |
| self.is_scale_input_called = False | |
| def scale_model_input( | |
| self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor] | |
| ) -> torch.FloatTensor: | |
| """ | |
| Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm. | |
| Args: | |
| sample (`torch.FloatTensor`): input sample | |
| timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain | |
| Returns: | |
| `torch.FloatTensor`: scaled input sample | |
| """ | |
| if isinstance(timestep, torch.Tensor): | |
| timestep = timestep.to(self.timesteps.device) | |
| step_index = (self.timesteps == timestep).nonzero().item() | |
| sigma = self.sigmas[step_index] | |
| sample = sample / ((sigma**2 + 1) ** 0.5) | |
| self.is_scale_input_called = True | |
| return sample | |
| def get_lms_coefficient(self, order, t, current_order): | |
| """ | |
| Compute a linear multistep coefficient. | |
| Args: | |
| order (TODO): | |
| t (TODO): | |
| current_order (TODO): | |
| """ | |
| def lms_derivative(tau): | |
| prod = 1.0 | |
| for k in range(order): | |
| if current_order == k: | |
| continue | |
| prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k]) | |
| return prod | |
| integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0] | |
| return integrated_coeff | |
| 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.config.num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy() | |
| sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
| sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) | |
| sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32) | |
| self.sigmas = torch.from_numpy(sigmas).to(device=device) | |
| if str(device).startswith("mps"): | |
| # mps does not support float64 | |
| self.timesteps = torch.from_numpy(timesteps).to(device, dtype=torch.float32) | |
| else: | |
| self.timesteps = torch.from_numpy(timesteps).to(device=device) | |
| self.derivatives = [] | |
| def step( | |
| self, | |
| model_output: torch.FloatTensor, | |
| timestep: Union[float, torch.FloatTensor], | |
| sample: torch.FloatTensor, | |
| order: int = 4, | |
| return_dict: bool = True, | |
| ) -> Union[LMSDiscreteSchedulerOutput, Tuple]: | |
| """ | |
| Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion | |
| process from the learned model outputs (most often the predicted noise). | |
| Args: | |
| model_output (`torch.FloatTensor`): direct output from learned diffusion model. | |
| timestep (`float`): current timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| current instance of sample being created by diffusion process. | |
| order: coefficient for multi-step inference. | |
| return_dict (`bool`): option for returning tuple rather than LMSDiscreteSchedulerOutput class | |
| Returns: | |
| [`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] or `tuple`: | |
| [`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. | |
| When returning a tuple, the first element is the sample tensor. | |
| """ | |
| if not self.is_scale_input_called: | |
| warnings.warn( | |
| "The `scale_model_input` function should be called before `step` to ensure correct denoising. " | |
| "See `StableDiffusionPipeline` for a usage example." | |
| ) | |
| if isinstance(timestep, torch.Tensor): | |
| timestep = timestep.to(self.timesteps.device) | |
| step_index = (self.timesteps == timestep).nonzero().item() | |
| sigma = self.sigmas[step_index] | |
| # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise | |
| if self.config.prediction_type == "epsilon": | |
| pred_original_sample = sample - sigma * model_output | |
| elif self.config.prediction_type == "v_prediction": | |
| # * c_out + input * c_skip | |
| pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1)) | |
| else: | |
| raise ValueError( | |
| f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" | |
| ) | |
| # 2. Convert to an ODE derivative | |
| derivative = (sample - pred_original_sample) / sigma | |
| self.derivatives.append(derivative) | |
| if len(self.derivatives) > order: | |
| self.derivatives.pop(0) | |
| # 3. Compute linear multistep coefficients | |
| order = min(step_index + 1, order) | |
| lms_coeffs = [self.get_lms_coefficient(order, step_index, curr_order) for curr_order in range(order)] | |
| # 4. Compute previous sample based on the derivatives path | |
| prev_sample = sample + sum( | |
| coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives)) | |
| ) | |
| if not return_dict: | |
| return (prev_sample,) | |
| return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample) | |
| def add_noise( | |
| self, | |
| original_samples: torch.FloatTensor, | |
| noise: torch.FloatTensor, | |
| timesteps: torch.FloatTensor, | |
| ) -> 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 = [(schedule_timesteps == t).nonzero().item() for t in timesteps] | |
| sigma = sigmas[step_indices].flatten() | |
| while len(sigma.shape) < len(original_samples.shape): | |
| sigma = sigma.unsqueeze(-1) | |
| noisy_samples = original_samples + noise * sigma | |
| return noisy_samples | |
| def __len__(self): | |
| return self.config.num_train_timesteps | |