# Copyright 2023 Stanford 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 code is strongly influenced by https://github.com/pesser/pytorch_diffusion # and https://github.com/hojonathanho/diffusion from dataclasses import dataclass from typing import Optional, Tuple, Union import flax import jax.numpy as jnp from ..configuration_utils import ConfigMixin, register_to_config from .scheduling_utils_flax import ( CommonSchedulerState, FlaxKarrasDiffusionSchedulers, FlaxSchedulerMixin, FlaxSchedulerOutput, add_noise_common, get_velocity_common, ) @flax.struct.dataclass class DDIMSchedulerState: common: CommonSchedulerState final_alpha_cumprod: jnp.ndarray # setable values init_noise_sigma: jnp.ndarray timesteps: jnp.ndarray num_inference_steps: Optional[int] = None @classmethod def create( cls, common: CommonSchedulerState, final_alpha_cumprod: jnp.ndarray, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, ): return cls( common=common, final_alpha_cumprod=final_alpha_cumprod, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) @dataclass class FlaxDDIMSchedulerOutput(FlaxSchedulerOutput): state: DDIMSchedulerState class FlaxDDIMScheduler(FlaxSchedulerMixin, ConfigMixin): """ Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. [`~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/2010.02502 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 (`jnp.ndarray`, optional): option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. clip_sample (`bool`, default `True`): option to clip predicted sample between -1 and 1 for numerical stability. set_alpha_to_one (`bool`, default `True`): 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. 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. 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. dtype (`jnp.dtype`, *optional*, defaults to `jnp.float32`): the `dtype` used for params and computation. """ _compatibles = [e.name for e in FlaxKarrasDiffusionSchedulers] dtype: jnp.dtype @property def has_state(self): return True @register_to_config 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, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", dtype: jnp.dtype = jnp.float32, ): self.dtype = dtype def create_state(self, common: Optional[CommonSchedulerState] = None) -> DDIMSchedulerState: if common is None: common = CommonSchedulerState.create(self) # At every step in ddim, we are looking into the previous alphas_cumprod # For the final step, there is no previous alphas_cumprod because we are already at 0 # `set_alpha_to_one` decides whether we set this parameter simply to one or # whether we use the final alpha of the "non-previous" one. final_alpha_cumprod = ( jnp.array(1.0, dtype=self.dtype) if self.config.set_alpha_to_one else common.alphas_cumprod[0] ) # standard deviation of the initial noise distribution init_noise_sigma = jnp.array(1.0, dtype=self.dtype) timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1] return DDIMSchedulerState.create( common=common, final_alpha_cumprod=final_alpha_cumprod, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) def scale_model_input( self, state: DDIMSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None ) -> jnp.ndarray: """ Args: state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` state data class instance. sample (`jnp.ndarray`): input sample timestep (`int`, optional): current timestep Returns: `jnp.ndarray`: scaled input sample """ return sample def set_timesteps( self, state: DDIMSchedulerState, num_inference_steps: int, shape: Tuple = () ) -> DDIMSchedulerState: """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference. Args: state (`DDIMSchedulerState`): the `FlaxDDIMScheduler` state data class instance. num_inference_steps (`int`): the number of diffusion steps used when generating samples with a pre-trained model. """ step_ratio = self.config.num_train_timesteps // num_inference_steps # creates integer timesteps by multiplying by ratio # rounding to avoid issues when num_inference_step is power of 3 timesteps = (jnp.arange(0, num_inference_steps) * step_ratio).round()[::-1] + self.config.steps_offset return state.replace( num_inference_steps=num_inference_steps, timesteps=timesteps, ) def _get_variance(self, state: DDIMSchedulerState, timestep, prev_timestep): alpha_prod_t = state.common.alphas_cumprod[timestep] alpha_prod_t_prev = jnp.where( prev_timestep >= 0, state.common.alphas_cumprod[prev_timestep], state.final_alpha_cumprod ) beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance def step( self, state: DDIMSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, eta: float = 0.0, return_dict: bool = True, ) -> Union[FlaxDDIMSchedulerOutput, 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 (`DDIMSchedulerState`): the `FlaxDDIMScheduler` 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. return_dict (`bool`): option for returning tuple rather than FlaxDDIMSchedulerOutput class Returns: [`FlaxDDIMSchedulerOutput`] or `tuple`: [`FlaxDDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ if state.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf # Ideally, read DDIM paper in-detail understanding # Notation ( -> # - pred_noise_t -> e_theta(x_t, t) # - pred_original_sample -> f_theta(x_t, t) or x_0 # - std_dev_t -> sigma_t # - eta -> η # - pred_sample_direction -> "direction pointing to x_t" # - pred_prev_sample -> "x_t-1" # 1. get previous step value (=t-1) prev_timestep = timestep - self.config.num_train_timesteps // state.num_inference_steps alphas_cumprod = state.common.alphas_cumprod final_alpha_cumprod = state.final_alpha_cumprod # 2. compute alphas, betas alpha_prod_t = alphas_cumprod[timestep] alpha_prod_t_prev = jnp.where(prev_timestep >= 0, alphas_cumprod[prev_timestep], final_alpha_cumprod) beta_prod_t = 1 - alpha_prod_t # 3. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) pred_epsilon = model_output elif self.config.prediction_type == "sample": pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`" ) # 4. compute variance: "sigma_t(η)" -> see formula (16) # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1) variance = self._get_variance(state, timestep, prev_timestep) std_dev_t = eta * variance ** (0.5) # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction if not return_dict: return (prev_sample, state) return FlaxDDIMSchedulerOutput(prev_sample=prev_sample, state=state) def add_noise( self, state: DDIMSchedulerState, original_samples: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return add_noise_common(state.common, original_samples, noise, timesteps) def get_velocity( self, state: DDIMSchedulerState, sample: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return get_velocity_common(state.common, sample, noise, timesteps) def __len__(self): return self.config.num_train_timesteps