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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. | |
| from typing import Optional, Tuple, Union | |
| import numpy as np | |
| import torch | |
| from scipy import integrate | |
| from ..configuration_utils import ConfigMixin, register_to_config | |
| from .scheduling_utils import SchedulerMixin, SchedulerOutput | |
| 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`. | |
| [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and | |
| [`~ConfigMixin.from_config`] functios. | |
| 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): TODO | |
| options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`, | |
| `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`. | |
| timestep_values (`np.ndarry`, optional): TODO | |
| tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays. | |
| """ | |
| 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, | |
| timestep_values: Optional[np.ndarray] = None, | |
| tensor_format: str = "pt", | |
| ): | |
| if trained_betas is not None: | |
| self.betas = np.asarray(trained_betas) | |
| if beta_schedule == "linear": | |
| self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32) | |
| elif beta_schedule == "scaled_linear": | |
| # this schedule is very specific to the latent diffusion model. | |
| self.betas = np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=np.float32) ** 2 | |
| else: | |
| raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}") | |
| self.alphas = 1.0 - self.betas | |
| self.alphas_cumprod = np.cumprod(self.alphas, axis=0) | |
| self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 | |
| # setable values | |
| self.num_inference_steps = None | |
| self.timesteps = np.arange(0, num_train_timesteps)[::-1].copy() | |
| self.derivatives = [] | |
| self.tensor_format = tensor_format | |
| self.set_format(tensor_format=tensor_format) | |
| 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): | |
| """ | |
| 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. | |
| """ | |
| self.num_inference_steps = num_inference_steps | |
| self.timesteps = np.linspace(self.num_train_timesteps - 1, 0, num_inference_steps, dtype=float) | |
| low_idx = np.floor(self.timesteps).astype(int) | |
| high_idx = np.ceil(self.timesteps).astype(int) | |
| frac = np.mod(self.timesteps, 1.0) | |
| sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
| sigmas = (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx] | |
| self.sigmas = np.concatenate([sigmas, [0.0]]) | |
| self.derivatives = [] | |
| self.set_format(tensor_format=self.tensor_format) | |
| def step( | |
| self, | |
| model_output: Union[torch.FloatTensor, np.ndarray], | |
| timestep: int, | |
| sample: Union[torch.FloatTensor, np.ndarray], | |
| order: int = 4, | |
| return_dict: bool = True, | |
| ) -> Union[SchedulerOutput, 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` or `np.ndarray`): direct output from learned diffusion model. | |
| timestep (`int`): current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor` or `np.ndarray`): | |
| current instance of sample being created by diffusion process. | |
| order: coefficient for multi-step inference. | |
| return_dict (`bool`): option for returning tuple rather than SchedulerOutput class | |
| Returns: | |
| [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`: | |
| [`~schedulers.scheduling_utils.SchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When | |
| returning a tuple, the first element is the sample tensor. | |
| """ | |
| sigma = self.sigmas[timestep] | |
| # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise | |
| pred_original_sample = sample - sigma * model_output | |
| # 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(timestep + 1, order) | |
| lms_coeffs = [self.get_lms_coefficient(order, timestep, 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 SchedulerOutput(prev_sample=prev_sample) | |
| def add_noise( | |
| self, | |
| original_samples: Union[torch.FloatTensor, np.ndarray], | |
| noise: Union[torch.FloatTensor, np.ndarray], | |
| timesteps: Union[torch.IntTensor, np.ndarray], | |
| ) -> Union[torch.FloatTensor, np.ndarray]: | |
| sigmas = self.match_shape(self.sigmas[timesteps], noise) | |
| noisy_samples = original_samples + noise * sigmas | |
| return noisy_samples | |
| def __len__(self): | |
| return self.config.num_train_timesteps | |