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| # Copyright 2022 Google Brain 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/yang-song/score_sde_pytorch | |
| from dataclasses import dataclass | |
| from typing import Optional, Tuple, Union | |
| import flax | |
| import jax.numpy as jnp | |
| from jax import random | |
| from ..configuration_utils import ConfigMixin, register_to_config | |
| from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left | |
| class ScoreSdeVeSchedulerState: | |
| # setable values | |
| timesteps: Optional[jnp.ndarray] = None | |
| discrete_sigmas: Optional[jnp.ndarray] = None | |
| sigmas: Optional[jnp.ndarray] = None | |
| def create(cls): | |
| return cls() | |
| class FlaxSdeVeOutput(FlaxSchedulerOutput): | |
| """ | |
| Output class for the ScoreSdeVeScheduler's step function output. | |
| Args: | |
| state (`ScoreSdeVeSchedulerState`): | |
| prev_sample (`jnp.ndarray` 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. | |
| prev_sample_mean (`jnp.ndarray` of shape `(batch_size, num_channels, height, width)` for images): | |
| Mean averaged `prev_sample`. Same as `prev_sample`, only mean-averaged over previous timesteps. | |
| """ | |
| state: ScoreSdeVeSchedulerState | |
| prev_sample: jnp.ndarray | |
| prev_sample_mean: Optional[jnp.ndarray] = None | |
| class FlaxScoreSdeVeScheduler(FlaxSchedulerMixin, ConfigMixin): | |
| """ | |
| The variance exploding stochastic differential equation (SDE) scheduler. | |
| For more information, see the original paper: 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. | |
| Args: | |
| num_train_timesteps (`int`): number of diffusion steps used to train the model. | |
| snr (`float`): | |
| coefficient weighting the step from the model_output sample (from the network) to the random noise. | |
| sigma_min (`float`): | |
| initial noise scale for sigma sequence in sampling procedure. The minimum sigma should mirror the | |
| distribution of the data. | |
| sigma_max (`float`): maximum value used for the range of continuous timesteps passed into the model. | |
| sampling_eps (`float`): the end value of sampling, where timesteps decrease progressively from 1 to | |
| epsilon. | |
| correct_steps (`int`): number of correction steps performed on a produced sample. | |
| """ | |
| def has_state(self): | |
| return True | |
| def __init__( | |
| self, | |
| num_train_timesteps: int = 2000, | |
| snr: float = 0.15, | |
| sigma_min: float = 0.01, | |
| sigma_max: float = 1348.0, | |
| sampling_eps: float = 1e-5, | |
| correct_steps: int = 1, | |
| ): | |
| pass | |
| def create_state(self): | |
| state = ScoreSdeVeSchedulerState.create() | |
| return self.set_sigmas( | |
| state, | |
| self.config.num_train_timesteps, | |
| self.config.sigma_min, | |
| self.config.sigma_max, | |
| self.config.sampling_eps, | |
| ) | |
| def set_timesteps( | |
| self, state: ScoreSdeVeSchedulerState, num_inference_steps: int, shape: Tuple = (), sampling_eps: float = None | |
| ) -> ScoreSdeVeSchedulerState: | |
| """ | |
| Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference. | |
| Args: | |
| state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance. | |
| num_inference_steps (`int`): | |
| the number of diffusion steps used when generating samples with a pre-trained model. | |
| sampling_eps (`float`, optional): final timestep value (overrides value given at Scheduler instantiation). | |
| """ | |
| sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps | |
| timesteps = jnp.linspace(1, sampling_eps, num_inference_steps) | |
| return state.replace(timesteps=timesteps) | |
| def set_sigmas( | |
| self, | |
| state: ScoreSdeVeSchedulerState, | |
| num_inference_steps: int, | |
| sigma_min: float = None, | |
| sigma_max: float = None, | |
| sampling_eps: float = None, | |
| ) -> ScoreSdeVeSchedulerState: | |
| """ | |
| Sets the noise scales used for the diffusion chain. Supporting function to be run before inference. | |
| The sigmas control the weight of the `drift` and `diffusion` components of sample update. | |
| Args: | |
| state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance. | |
| num_inference_steps (`int`): | |
| the number of diffusion steps used when generating samples with a pre-trained model. | |
| sigma_min (`float`, optional): | |
| initial noise scale value (overrides value given at Scheduler instantiation). | |
| sigma_max (`float`, optional): final noise scale value (overrides value given at Scheduler instantiation). | |
| sampling_eps (`float`, optional): final timestep value (overrides value given at Scheduler instantiation). | |
| """ | |
| sigma_min = sigma_min if sigma_min is not None else self.config.sigma_min | |
| sigma_max = sigma_max if sigma_max is not None else self.config.sigma_max | |
| sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps | |
| if state.timesteps is None: | |
| state = self.set_timesteps(state, num_inference_steps, sampling_eps) | |
| discrete_sigmas = jnp.exp(jnp.linspace(jnp.log(sigma_min), jnp.log(sigma_max), num_inference_steps)) | |
| sigmas = jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]) | |
| return state.replace(discrete_sigmas=discrete_sigmas, sigmas=sigmas) | |
| def get_adjacent_sigma(self, state, timesteps, t): | |
| return jnp.where(timesteps == 0, jnp.zeros_like(t), state.discrete_sigmas[timesteps - 1]) | |
| def step_pred( | |
| self, | |
| state: ScoreSdeVeSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| key: random.KeyArray, | |
| return_dict: bool = True, | |
| ) -> Union[FlaxSdeVeOutput, 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: | |
| state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance. | |
| model_output (`jnp.ndarray`): direct output from learned diffusion model. | |
| timestep (`int`): current discrete timestep in the diffusion chain. | |
| sample (`jnp.ndarray`): | |
| current instance of sample being created by diffusion process. | |
| generator: random number generator. | |
| return_dict (`bool`): option for returning tuple rather than FlaxSdeVeOutput class | |
| Returns: | |
| [`FlaxSdeVeOutput`] or `tuple`: [`FlaxSdeVeOutput`] if `return_dict` is True, otherwise a `tuple`. When | |
| returning a tuple, the first element is the sample tensor. | |
| """ | |
| if state.timesteps is None: | |
| raise ValueError( | |
| "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler" | |
| ) | |
| timestep = timestep * jnp.ones( | |
| sample.shape[0], | |
| ) | |
| timesteps = (timestep * (len(state.timesteps) - 1)).long() | |
| sigma = state.discrete_sigmas[timesteps] | |
| adjacent_sigma = self.get_adjacent_sigma(state, timesteps, timestep) | |
| drift = jnp.zeros_like(sample) | |
| diffusion = (sigma**2 - adjacent_sigma**2) ** 0.5 | |
| # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x) | |
| # also equation 47 shows the analog from SDE models to ancestral sampling methods | |
| diffusion = diffusion.flatten() | |
| diffusion = broadcast_to_shape_from_left(diffusion, sample.shape) | |
| drift = drift - diffusion**2 * model_output | |
| # equation 6: sample noise for the diffusion term of | |
| key = random.split(key, num=1) | |
| noise = random.normal(key=key, shape=sample.shape) | |
| prev_sample_mean = sample - drift # subtract because `dt` is a small negative timestep | |
| # TODO is the variable diffusion the correct scaling term for the noise? | |
| prev_sample = prev_sample_mean + diffusion * noise # add impact of diffusion field g | |
| if not return_dict: | |
| return (prev_sample, prev_sample_mean, state) | |
| return FlaxSdeVeOutput(prev_sample=prev_sample, prev_sample_mean=prev_sample_mean, state=state) | |
| def step_correct( | |
| self, | |
| state: ScoreSdeVeSchedulerState, | |
| model_output: jnp.ndarray, | |
| sample: jnp.ndarray, | |
| key: random.KeyArray, | |
| return_dict: bool = True, | |
| ) -> Union[FlaxSdeVeOutput, Tuple]: | |
| """ | |
| Correct the predicted sample based on the output model_output of the network. This is often run repeatedly | |
| after making the prediction for the previous timestep. | |
| Args: | |
| state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance. | |
| model_output (`jnp.ndarray`): direct output from learned diffusion model. | |
| sample (`jnp.ndarray`): | |
| current instance of sample being created by diffusion process. | |
| generator: random number generator. | |
| return_dict (`bool`): option for returning tuple rather than FlaxSdeVeOutput class | |
| Returns: | |
| [`FlaxSdeVeOutput`] or `tuple`: [`FlaxSdeVeOutput`] if `return_dict` is True, otherwise a `tuple`. When | |
| returning a tuple, the first element is the sample tensor. | |
| """ | |
| if state.timesteps is None: | |
| raise ValueError( | |
| "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler" | |
| ) | |
| # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z" | |
| # sample noise for correction | |
| key = random.split(key, num=1) | |
| noise = random.normal(key=key, shape=sample.shape) | |
| # compute step size from the model_output, the noise, and the snr | |
| grad_norm = jnp.linalg.norm(model_output) | |
| noise_norm = jnp.linalg.norm(noise) | |
| step_size = (self.config.snr * noise_norm / grad_norm) ** 2 * 2 | |
| step_size = step_size * jnp.ones(sample.shape[0]) | |
| # compute corrected sample: model_output term and noise term | |
| step_size = step_size.flatten() | |
| step_size = broadcast_to_shape_from_left(step_size, sample.shape) | |
| prev_sample_mean = sample + step_size * model_output | |
| prev_sample = prev_sample_mean + ((step_size * 2) ** 0.5) * noise | |
| if not return_dict: | |
| return (prev_sample, state) | |
| return FlaxSdeVeOutput(prev_sample=prev_sample, state=state) | |
| def __len__(self): | |
| return self.config.num_train_timesteps | |