# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved. # Copyright 2022 NVIDIA 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 dataclasses import dataclass from typing import Optional, Tuple, Union import numpy as np import paddle from ..configuration_utils import ConfigMixin, register_to_config from ..utils import BaseOutput from .scheduling_utils import SchedulerMixin @dataclass class KarrasVeOutput(BaseOutput): """ Output class for the scheduler's step function output. Args: prev_sample (`paddle.Tensor` 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. derivative (`paddle.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Derivative of predicted original image sample (x_0). pred_original_sample (`paddle.Tensor` 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: paddle.Tensor derivative: paddle.Tensor pred_original_sample: Optional[paddle.Tensor] = None class KarrasVeScheduler(SchedulerMixin, ConfigMixin): """ Stochastic sampling from Karras et al. [1] tailored to the Variance-Expanding (VE) models [2]. Use Algorithm 2 and the VE column of Table 1 from [1] for reference. [1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364 [2] Song, Yang, et al. "Score-based generative modeling through stochastic differential equations." https://arxiv.org/abs/2011.13456 [`~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. For more details on the parameters, see the original paper's Appendix E.: "Elucidating the Design Space of Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364. The grid search values used to find the optimal {s_noise, s_churn, s_min, s_max} for a specific model are described in Table 5 of the paper. Args: sigma_min (`float`): minimum noise magnitude sigma_max (`float`): maximum noise magnitude s_noise (`float`): the amount of additional noise to counteract loss of detail during sampling. A reasonable range is [1.000, 1.011]. s_churn (`float`): the parameter controlling the overall amount of stochasticity. A reasonable range is [0, 100]. s_min (`float`): the start value of the sigma range where we add noise (enable stochasticity). A reasonable range is [0, 10]. s_max (`float`): the end value of the sigma range where we add noise. A reasonable range is [0.2, 80]. """ order = 2 @register_to_config def __init__( self, sigma_min: float = 0.02, sigma_max: float = 100, s_noise: float = 1.007, s_churn: float = 80, s_min: float = 0.05, s_max: float = 50, ): # standard deviation of the initial noise distribution self.init_noise_sigma = sigma_max # setable values self.num_inference_steps: int = None self.timesteps: paddle.Tensor = None self.schedule: paddle.Tensor = None # sigma(t_i) def scale_model_input(self, sample: paddle.Tensor, timestep: Optional[int] = None) -> paddle.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: sample (`paddle.Tensor`): input sample timestep (`int`, optional): current timestep Returns: `paddle.Tensor`: scaled input sample """ return sample def set_timesteps(self, num_inference_steps: int): """ Sets the continuous 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 timesteps = np.arange(0, self.num_inference_steps)[::-1].copy() self.timesteps = paddle.to_tensor(timesteps) schedule = [ ( self.config.sigma_max**2 * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1)) ) for i in self.timesteps ] self.schedule = paddle.to_tensor(schedule, dtype="float32") def add_noise_to_input( self, sample: paddle.Tensor, sigma: float, generator: Optional[paddle.Generator] = None ) -> Tuple[paddle.Tensor, float]: """ Explicit Langevin-like "churn" step of adding noise to the sample according to a factor gamma_i ≥ 0 to reach a higher noise level sigma_hat = sigma_i + gamma_i*sigma_i. TODO Args: """ if self.config.s_min <= sigma <= self.config.s_max: gamma = min(self.config.s_churn / self.num_inference_steps, 2**0.5 - 1) else: gamma = 0 # sample eps ~ N(0, S_noise^2 * I) eps = self.config.s_noise * paddle.randn(sample.shape, generator=generator) sigma_hat = sigma + gamma * sigma sample_hat = sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps) return sample_hat, sigma_hat def step( self, model_output: paddle.Tensor, sigma_hat: float, sigma_prev: float, sample_hat: paddle.Tensor, return_dict: bool = True, ) -> Union[KarrasVeOutput, 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 (`paddle.Tensor`): direct output from learned diffusion model. sigma_hat (`float`): TODO sigma_prev (`float`): TODO sample_hat (`paddle.Tensor`): TODO return_dict (`bool`): option for returning tuple rather than KarrasVeOutput class KarrasVeOutput: updated sample in the diffusion chain and derivative (TODO double check). Returns: [`~schedulers.scheduling_karras_ve.KarrasVeOutput`] or `tuple`: [`~schedulers.scheduling_karras_ve.KarrasVeOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ pred_original_sample = sample_hat + sigma_hat * model_output derivative = (sample_hat - pred_original_sample) / sigma_hat sample_prev = sample_hat + (sigma_prev - sigma_hat) * derivative if not return_dict: return (sample_prev, derivative) return KarrasVeOutput( prev_sample=sample_prev, derivative=derivative, pred_original_sample=pred_original_sample ) def step_correct( self, model_output: paddle.Tensor, sigma_hat: float, sigma_prev: float, sample_hat: paddle.Tensor, sample_prev: paddle.Tensor, derivative: paddle.Tensor, return_dict: bool = True, ) -> Union[KarrasVeOutput, Tuple]: """ Correct the predicted sample based on the output model_output of the network. TODO complete description Args: model_output (`paddle.Tensor`): direct output from learned diffusion model. sigma_hat (`float`): TODO sigma_prev (`float`): TODO sample_hat (`paddle.Tensor`): TODO sample_prev (`paddle.Tensor`): TODO derivative (`paddle.Tensor`): TODO return_dict (`bool`): option for returning tuple rather than KarrasVeOutput class Returns: prev_sample (TODO): updated sample in the diffusion chain. derivative (TODO): TODO """ pred_original_sample = sample_prev + sigma_prev * model_output derivative_corr = (sample_prev - pred_original_sample) / sigma_prev sample_prev = sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr) if not return_dict: return (sample_prev, derivative) return KarrasVeOutput( prev_sample=sample_prev, derivative=derivative, pred_original_sample=pred_original_sample ) def add_noise(self, original_samples, noise, timesteps): raise NotImplementedError()