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| # Copyright 2022 Zhejiang University 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/ermongroup/ddim | |
| 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 _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS | |
| from .scheduling_utils import SchedulerMixin, SchedulerOutput | |
| def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999): | |
| """ | |
| 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. | |
| Returns: | |
| betas (`np.ndarray`): the betas used by the scheduler to step the model outputs | |
| """ | |
| def alpha_bar(time_step): | |
| return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2 | |
| 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(t2) / alpha_bar(t1), max_beta)) | |
| return torch.tensor(betas, dtype=torch.float32) | |
| class PNDMScheduler(SchedulerMixin, ConfigMixin): | |
| """ | |
| Pseudo numerical methods for diffusion models (PNDM) proposes using more advanced ODE integration techniques, | |
| namely Runge-Kutta method and a linear multi-step method. | |
| [`~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, see the original paper: https://arxiv.org/abs/2202.09778 | |
| 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`, `scaled_linear`, or `squaredcos_cap_v2`. | |
| trained_betas (`np.ndarray`, optional): | |
| option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. | |
| skip_prk_steps (`bool`): | |
| allows the scheduler to skip the Runge-Kutta steps that are defined in the original paper as being required | |
| before plms steps; defaults to `False`. | |
| set_alpha_to_one (`bool`, default `False`): | |
| each diffusion step uses the value of alphas product at that step and at the previous one. For the final | |
| step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`, | |
| otherwise it uses the value of alpha at step 0. | |
| 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) | |
| steps_offset (`int`, default `0`): | |
| an offset added to the inference steps. You can use a combination of `offset=1` and | |
| `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in | |
| stable diffusion. | |
| """ | |
| _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, | |
| skip_prk_steps: bool = False, | |
| set_alpha_to_one: bool = False, | |
| prediction_type: str = "epsilon", | |
| steps_offset: int = 0, | |
| ): | |
| 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) | |
| self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0] | |
| # standard deviation of the initial noise distribution | |
| self.init_noise_sigma = 1.0 | |
| # For now we only support F-PNDM, i.e. the runge-kutta method | |
| # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf | |
| # mainly at formula (9), (12), (13) and the Algorithm 2. | |
| self.pndm_order = 4 | |
| # running values | |
| self.cur_model_output = 0 | |
| self.counter = 0 | |
| self.cur_sample = None | |
| self.ets = [] | |
| # setable values | |
| self.num_inference_steps = None | |
| self._timesteps = np.arange(0, num_train_timesteps)[::-1].copy() | |
| self.prk_timesteps = None | |
| self.plms_timesteps = None | |
| self.timesteps = None | |
| def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None): | |
| """ | |
| Sets the discrete 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 | |
| step_ratio = self.config.num_train_timesteps // self.num_inference_steps | |
| # creates integer timesteps by multiplying by ratio | |
| # casting to int to avoid issues when num_inference_step is power of 3 | |
| self._timesteps = (np.arange(0, num_inference_steps) * step_ratio).round() | |
| self._timesteps += self.config.steps_offset | |
| if self.config.skip_prk_steps: | |
| # for some models like stable diffusion the prk steps can/should be skipped to | |
| # produce better results. When using PNDM with `self.config.skip_prk_steps` the implementation | |
| # is based on crowsonkb's PLMS sampler implementation: https://github.com/CompVis/latent-diffusion/pull/51 | |
| self.prk_timesteps = np.array([]) | |
| self.plms_timesteps = np.concatenate([self._timesteps[:-1], self._timesteps[-2:-1], self._timesteps[-1:]])[ | |
| ::-1 | |
| ].copy() | |
| else: | |
| prk_timesteps = np.array(self._timesteps[-self.pndm_order :]).repeat(2) + np.tile( | |
| np.array([0, self.config.num_train_timesteps // num_inference_steps // 2]), self.pndm_order | |
| ) | |
| self.prk_timesteps = (prk_timesteps[:-1].repeat(2)[1:-1])[::-1].copy() | |
| self.plms_timesteps = self._timesteps[:-3][ | |
| ::-1 | |
| ].copy() # we copy to avoid having negative strides which are not supported by torch.from_numpy | |
| timesteps = np.concatenate([self.prk_timesteps, self.plms_timesteps]).astype(np.int64) | |
| self.timesteps = torch.from_numpy(timesteps).to(device) | |
| self.ets = [] | |
| self.counter = 0 | |
| def step( | |
| self, | |
| model_output: torch.FloatTensor, | |
| timestep: int, | |
| sample: torch.FloatTensor, | |
| 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). | |
| This function calls `step_prk()` or `step_plms()` depending on the internal variable `counter`. | |
| Args: | |
| model_output (`torch.FloatTensor`): direct output from learned diffusion model. | |
| timestep (`int`): current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| current instance of sample being created by diffusion process. | |
| 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. | |
| """ | |
| if self.counter < len(self.prk_timesteps) and not self.config.skip_prk_steps: | |
| return self.step_prk(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict) | |
| else: | |
| return self.step_plms(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict) | |
| def step_prk( | |
| self, | |
| model_output: torch.FloatTensor, | |
| timestep: int, | |
| sample: torch.FloatTensor, | |
| return_dict: bool = True, | |
| ) -> Union[SchedulerOutput, Tuple]: | |
| """ | |
| Step function propagating the sample with the Runge-Kutta method. RK takes 4 forward passes to approximate the | |
| solution to the differential equation. | |
| Args: | |
| model_output (`torch.FloatTensor`): direct output from learned diffusion model. | |
| timestep (`int`): current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| current instance of sample being created by diffusion process. | |
| return_dict (`bool`): option for returning tuple rather than SchedulerOutput class | |
| Returns: | |
| [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is | |
| True, otherwise a `tuple`. When returning a tuple, 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" | |
| ) | |
| diff_to_prev = 0 if self.counter % 2 else self.config.num_train_timesteps // self.num_inference_steps // 2 | |
| prev_timestep = timestep - diff_to_prev | |
| timestep = self.prk_timesteps[self.counter // 4 * 4] | |
| if self.counter % 4 == 0: | |
| self.cur_model_output += 1 / 6 * model_output | |
| self.ets.append(model_output) | |
| self.cur_sample = sample | |
| elif (self.counter - 1) % 4 == 0: | |
| self.cur_model_output += 1 / 3 * model_output | |
| elif (self.counter - 2) % 4 == 0: | |
| self.cur_model_output += 1 / 3 * model_output | |
| elif (self.counter - 3) % 4 == 0: | |
| model_output = self.cur_model_output + 1 / 6 * model_output | |
| self.cur_model_output = 0 | |
| # cur_sample should not be `None` | |
| cur_sample = self.cur_sample if self.cur_sample is not None else sample | |
| prev_sample = self._get_prev_sample(cur_sample, timestep, prev_timestep, model_output) | |
| self.counter += 1 | |
| if not return_dict: | |
| return (prev_sample,) | |
| return SchedulerOutput(prev_sample=prev_sample) | |
| def step_plms( | |
| self, | |
| model_output: torch.FloatTensor, | |
| timestep: int, | |
| sample: torch.FloatTensor, | |
| return_dict: bool = True, | |
| ) -> Union[SchedulerOutput, Tuple]: | |
| """ | |
| Step function propagating the sample with the linear multi-step method. This has one forward pass with multiple | |
| times to approximate the solution. | |
| Args: | |
| model_output (`torch.FloatTensor`): direct output from learned diffusion model. | |
| timestep (`int`): current discrete timestep in the diffusion chain. | |
| sample (`torch.FloatTensor`): | |
| current instance of sample being created by diffusion process. | |
| return_dict (`bool`): option for returning tuple rather than SchedulerOutput class | |
| Returns: | |
| [`~scheduling_utils.SchedulerOutput`] or `tuple`: [`~scheduling_utils.SchedulerOutput`] if `return_dict` is | |
| True, otherwise a `tuple`. When returning a tuple, 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 not self.config.skip_prk_steps and len(self.ets) < 3: | |
| raise ValueError( | |
| f"{self.__class__} can only be run AFTER scheduler has been run " | |
| "in 'prk' mode for at least 12 iterations " | |
| "See: https://github.com/huggingface/diffusers/blob/main/src/diffusers/pipelines/pipeline_pndm.py " | |
| "for more information." | |
| ) | |
| prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps | |
| if self.counter != 1: | |
| self.ets = self.ets[-3:] | |
| self.ets.append(model_output) | |
| else: | |
| prev_timestep = timestep | |
| timestep = timestep + self.config.num_train_timesteps // self.num_inference_steps | |
| if len(self.ets) == 1 and self.counter == 0: | |
| model_output = model_output | |
| self.cur_sample = sample | |
| elif len(self.ets) == 1 and self.counter == 1: | |
| model_output = (model_output + self.ets[-1]) / 2 | |
| sample = self.cur_sample | |
| self.cur_sample = None | |
| elif len(self.ets) == 2: | |
| model_output = (3 * self.ets[-1] - self.ets[-2]) / 2 | |
| elif len(self.ets) == 3: | |
| model_output = (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12 | |
| else: | |
| model_output = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4]) | |
| prev_sample = self._get_prev_sample(sample, timestep, prev_timestep, model_output) | |
| self.counter += 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`): input sample | |
| Returns: | |
| `torch.FloatTensor`: scaled input sample | |
| """ | |
| return sample | |
| def _get_prev_sample(self, sample, timestep, prev_timestep, model_output): | |
| # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf | |
| # this function computes x_(t−δ) using the formula of (9) | |
| # Note that x_t needs to be added to both sides of the equation | |
| # Notation (<variable name> -> <name in paper> | |
| # alpha_prod_t -> α_t | |
| # alpha_prod_t_prev -> α_(t−δ) | |
| # beta_prod_t -> (1 - α_t) | |
| # beta_prod_t_prev -> (1 - α_(t−δ)) | |
| # sample -> x_t | |
| # model_output -> e_θ(x_t, t) | |
| # prev_sample -> x_(t−δ) | |
| alpha_prod_t = self.alphas_cumprod[timestep] | |
| alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod | |
| beta_prod_t = 1 - alpha_prod_t | |
| beta_prod_t_prev = 1 - alpha_prod_t_prev | |
| if self.config.prediction_type == "v_prediction": | |
| model_output = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample | |
| elif self.config.prediction_type != "epsilon": | |
| raise ValueError( | |
| f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `v_prediction`" | |
| ) | |
| # corresponds to (α_(t−δ) - α_t) divided by | |
| # denominator of x_t in formula (9) and plus 1 | |
| # Note: (α_(t−δ) - α_t) / (sqrt(α_t) * (sqrt(α_(t−δ)) + sqr(α_t))) = | |
| # sqrt(α_(t−δ)) / sqrt(α_t)) | |
| sample_coeff = (alpha_prod_t_prev / alpha_prod_t) ** (0.5) | |
| # corresponds to denominator of e_θ(x_t, t) in formula (9) | |
| model_output_denom_coeff = alpha_prod_t * beta_prod_t_prev ** (0.5) + ( | |
| alpha_prod_t * beta_prod_t * alpha_prod_t_prev | |
| ) ** (0.5) | |
| # full formula (9) | |
| prev_sample = ( | |
| sample_coeff * sample - (alpha_prod_t_prev - alpha_prod_t) * model_output / model_output_denom_coeff | |
| ) | |
| return prev_sample | |
| def add_noise( | |
| self, | |
| original_samples: torch.FloatTensor, | |
| noise: torch.FloatTensor, | |
| timesteps: torch.IntTensor, | |
| ) -> torch.Tensor: | |
| # Make sure alphas_cumprod and timestep have same device and dtype as original_samples | |
| self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype) | |
| timesteps = timesteps.to(original_samples.device) | |
| sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5 | |
| sqrt_alpha_prod = sqrt_alpha_prod.flatten() | |
| while len(sqrt_alpha_prod.shape) < len(original_samples.shape): | |
| sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1) | |
| sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5 | |
| sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() | |
| while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape): | |
| sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) | |
| noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise | |
| return noisy_samples | |
| def __len__(self): | |
| return self.config.num_train_timesteps | |