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| # Copyright 2022 UC Berkeley 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 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, FrozenDict, register_to_config | |
| from ..utils import deprecate | |
| from .scheduling_utils_flax import ( | |
| _FLAX_COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS, | |
| FlaxSchedulerMixin, | |
| FlaxSchedulerOutput, | |
| broadcast_to_shape_from_left, | |
| ) | |
| def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999) -> jnp.ndarray: | |
| """ | |
| 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 (`jnp.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 jnp.array(betas, dtype=jnp.float32) | |
| class DDPMSchedulerState: | |
| # setable values | |
| timesteps: jnp.ndarray | |
| num_inference_steps: Optional[int] = None | |
| def create(cls, num_train_timesteps: int): | |
| return cls(timesteps=jnp.arange(0, num_train_timesteps)[::-1]) | |
| class FlaxDDPMSchedulerOutput(FlaxSchedulerOutput): | |
| state: DDPMSchedulerState | |
| class FlaxDDPMScheduler(FlaxSchedulerMixin, ConfigMixin): | |
| """ | |
| Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and | |
| Langevin dynamics sampling. | |
| [`~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/2006.11239 | |
| 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. | |
| variance_type (`str`): | |
| 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`. | |
| clip_sample (`bool`, default `True`): | |
| option to clip predicted sample between -1 and 1 for numerical stability. | |
| prediction_type (`str`, default `epsilon`): | |
| indicates whether the model predicts the noise (epsilon), or the samples. One of `epsilon`, `sample`. | |
| `v-prediction` is not supported for this scheduler. | |
| """ | |
| _compatibles = _FLAX_COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy() | |
| _deprecated_kwargs = ["predict_epsilon"] | |
| def has_state(self): | |
| return True | |
| 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[jnp.ndarray] = None, | |
| variance_type: str = "fixed_small", | |
| clip_sample: bool = True, | |
| prediction_type: str = "epsilon", | |
| **kwargs, | |
| ): | |
| message = ( | |
| "Please make sure to instantiate your scheduler with `prediction_type` instead. E.g. `scheduler =" | |
| " FlaxDDPMScheduler.from_pretrained(<model_id>, prediction_type='epsilon')`." | |
| ) | |
| predict_epsilon = deprecate("predict_epsilon", "0.11.0", message, take_from=kwargs) | |
| if predict_epsilon is not None: | |
| self.register_to_config(prediction_type="epsilon" if predict_epsilon else "sample") | |
| if trained_betas is not None: | |
| self.betas = jnp.asarray(trained_betas) | |
| elif beta_schedule == "linear": | |
| self.betas = jnp.linspace(beta_start, beta_end, num_train_timesteps, dtype=jnp.float32) | |
| elif beta_schedule == "scaled_linear": | |
| # this schedule is very specific to the latent diffusion model. | |
| self.betas = jnp.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=jnp.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 = jnp.cumprod(self.alphas, axis=0) | |
| self.one = jnp.array(1.0) | |
| def create_state(self): | |
| return DDPMSchedulerState.create(num_train_timesteps=self.config.num_train_timesteps) | |
| def set_timesteps( | |
| self, state: DDPMSchedulerState, num_inference_steps: int, shape: Tuple = () | |
| ) -> DDPMSchedulerState: | |
| """ | |
| Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference. | |
| Args: | |
| state (`DDIMSchedulerState`): | |
| the `FlaxDDPMScheduler` state data class instance. | |
| num_inference_steps (`int`): | |
| the number of diffusion steps used when generating samples with a pre-trained model. | |
| """ | |
| num_inference_steps = min(self.config.num_train_timesteps, num_inference_steps) | |
| timesteps = jnp.arange( | |
| 0, self.config.num_train_timesteps, self.config.num_train_timesteps // num_inference_steps | |
| )[::-1] | |
| return state.replace(num_inference_steps=num_inference_steps, timesteps=timesteps) | |
| def _get_variance(self, t, predicted_variance=None, variance_type=None): | |
| alpha_prod_t = self.alphas_cumprod[t] | |
| alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one | |
| # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf) | |
| # and sample from it to get previous sample | |
| # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample | |
| variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t] | |
| if variance_type is None: | |
| variance_type = self.config.variance_type | |
| # hacks - were probably added for training stability | |
| if variance_type == "fixed_small": | |
| variance = jnp.clip(variance, a_min=1e-20) | |
| # for rl-diffuser https://arxiv.org/abs/2205.09991 | |
| elif variance_type == "fixed_small_log": | |
| variance = jnp.log(jnp.clip(variance, a_min=1e-20)) | |
| elif variance_type == "fixed_large": | |
| variance = self.betas[t] | |
| elif variance_type == "fixed_large_log": | |
| # Glide max_log | |
| variance = jnp.log(self.betas[t]) | |
| elif variance_type == "learned": | |
| return predicted_variance | |
| elif variance_type == "learned_range": | |
| min_log = variance | |
| max_log = self.betas[t] | |
| frac = (predicted_variance + 1) / 2 | |
| variance = frac * max_log + (1 - frac) * min_log | |
| return variance | |
| def step( | |
| self, | |
| state: DDPMSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| key: random.KeyArray, | |
| return_dict: bool = True, | |
| **kwargs, | |
| ) -> Union[FlaxDDPMSchedulerOutput, 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 (`DDPMSchedulerState`): the `FlaxDDPMScheduler` 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. | |
| key (`random.KeyArray`): a PRNG key. | |
| return_dict (`bool`): option for returning tuple rather than FlaxDDPMSchedulerOutput class | |
| Returns: | |
| [`FlaxDDPMSchedulerOutput`] or `tuple`: [`FlaxDDPMSchedulerOutput`] if `return_dict` is True, otherwise a | |
| `tuple`. When returning a tuple, the first element is the sample tensor. | |
| """ | |
| message = ( | |
| "Please make sure to instantiate your scheduler with `prediction_type` instead. E.g. `scheduler =" | |
| " FlaxDDPMScheduler.from_pretrained(<model_id>, prediction_type='epsilon')`." | |
| ) | |
| predict_epsilon = deprecate("predict_epsilon", "0.11.0", message, take_from=kwargs) | |
| if predict_epsilon is not None: | |
| new_config = dict(self.config) | |
| new_config["prediction_type"] = "epsilon" if predict_epsilon else "sample" | |
| self._internal_dict = FrozenDict(new_config) | |
| t = timestep | |
| if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]: | |
| model_output, predicted_variance = jnp.split(model_output, sample.shape[1], axis=1) | |
| else: | |
| predicted_variance = None | |
| # 1. compute alphas, betas | |
| alpha_prod_t = self.alphas_cumprod[t] | |
| alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one | |
| beta_prod_t = 1 - alpha_prod_t | |
| beta_prod_t_prev = 1 - alpha_prod_t_prev | |
| # 2. compute predicted original sample from predicted noise also called | |
| # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf | |
| if self.config.prediction_type == "epsilon": | |
| pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) | |
| elif self.config.prediction_type == "sample": | |
| pred_original_sample = model_output | |
| else: | |
| raise ValueError( | |
| f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` " | |
| " for the FlaxDDPMScheduler." | |
| ) | |
| # 3. Clip "predicted x_0" | |
| if self.config.clip_sample: | |
| pred_original_sample = jnp.clip(pred_original_sample, -1, 1) | |
| # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t | |
| # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf | |
| pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * self.betas[t]) / beta_prod_t | |
| current_sample_coeff = self.alphas[t] ** (0.5) * beta_prod_t_prev / beta_prod_t | |
| # 5. Compute predicted previous sample µ_t | |
| # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf | |
| pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample | |
| # 6. Add noise | |
| variance = 0 | |
| if t > 0: | |
| key = random.split(key, num=1) | |
| noise = random.normal(key=key, shape=model_output.shape) | |
| variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * noise | |
| pred_prev_sample = pred_prev_sample + variance | |
| if not return_dict: | |
| return (pred_prev_sample, state) | |
| return FlaxDDPMSchedulerOutput(prev_sample=pred_prev_sample, state=state) | |
| def add_noise( | |
| self, | |
| original_samples: jnp.ndarray, | |
| noise: jnp.ndarray, | |
| timesteps: jnp.ndarray, | |
| ) -> jnp.ndarray: | |
| sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5 | |
| sqrt_alpha_prod = sqrt_alpha_prod.flatten() | |
| sqrt_alpha_prod = broadcast_to_shape_from_left(sqrt_alpha_prod, original_samples.shape) | |
| sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5 | |
| sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() | |
| sqrt_one_minus_alpha_prod = broadcast_to_shape_from_left(sqrt_one_minus_alpha_prod, original_samples.shape) | |
| 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 | |