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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 dataclasses import dataclass | |
| from typing import Optional, Tuple, Union | |
| import flax | |
| import jax | |
| import jax.numpy as jnp | |
| from ..configuration_utils import ConfigMixin, register_to_config | |
| 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: int, 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 PNDMSchedulerState: | |
| # setable values | |
| _timesteps: jnp.ndarray | |
| num_inference_steps: Optional[int] = None | |
| prk_timesteps: Optional[jnp.ndarray] = None | |
| plms_timesteps: Optional[jnp.ndarray] = None | |
| timesteps: Optional[jnp.ndarray] = None | |
| # running values | |
| cur_model_output: Optional[jnp.ndarray] = None | |
| counter: int = 0 | |
| cur_sample: Optional[jnp.ndarray] = None | |
| ets: jnp.ndarray = jnp.array([]) | |
| def create(cls, num_train_timesteps: int): | |
| return cls(_timesteps=jnp.arange(0, num_train_timesteps)[::-1]) | |
| class FlaxPNDMSchedulerOutput(FlaxSchedulerOutput): | |
| state: PNDMSchedulerState | |
| class FlaxPNDMScheduler(FlaxSchedulerMixin, 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 (`jnp.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. | |
| 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 = _FLAX_COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy() | |
| 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, | |
| skip_prk_steps: bool = False, | |
| set_alpha_to_one: bool = False, | |
| steps_offset: int = 0, | |
| ): | |
| 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.final_alpha_cumprod = jnp.array(1.0) if set_alpha_to_one else self.alphas_cumprod[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 | |
| # standard deviation of the initial noise distribution | |
| self.init_noise_sigma = 1.0 | |
| def create_state(self): | |
| return PNDMSchedulerState.create(num_train_timesteps=self.config.num_train_timesteps) | |
| def set_timesteps(self, state: PNDMSchedulerState, num_inference_steps: int, shape: Tuple) -> PNDMSchedulerState: | |
| """ | |
| Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference. | |
| Args: | |
| state (`PNDMSchedulerState`): | |
| the `FlaxPNDMScheduler` state data class instance. | |
| num_inference_steps (`int`): | |
| the number of diffusion steps used when generating samples with a pre-trained model. | |
| shape (`Tuple`): | |
| the shape of the samples to be generated. | |
| """ | |
| offset = self.config.steps_offset | |
| 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() + offset | |
| state = state.replace(num_inference_steps=num_inference_steps, _timesteps=_timesteps) | |
| 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 | |
| state = state.replace( | |
| prk_timesteps=jnp.array([]), | |
| plms_timesteps=jnp.concatenate( | |
| [state._timesteps[:-1], state._timesteps[-2:-1], state._timesteps[-1:]] | |
| )[::-1], | |
| ) | |
| else: | |
| prk_timesteps = jnp.array(state._timesteps[-self.pndm_order :]).repeat(2) + jnp.tile( | |
| jnp.array([0, self.config.num_train_timesteps // num_inference_steps // 2]), self.pndm_order | |
| ) | |
| state = state.replace( | |
| prk_timesteps=(prk_timesteps[:-1].repeat(2)[1:-1])[::-1], | |
| plms_timesteps=state._timesteps[:-3][::-1], | |
| ) | |
| return state.replace( | |
| timesteps=jnp.concatenate([state.prk_timesteps, state.plms_timesteps]).astype(jnp.int32), | |
| counter=0, | |
| # Reserve space for the state variables | |
| cur_model_output=jnp.zeros(shape), | |
| cur_sample=jnp.zeros(shape), | |
| ets=jnp.zeros((4,) + shape), | |
| ) | |
| def scale_model_input( | |
| self, state: PNDMSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None | |
| ) -> jnp.ndarray: | |
| """ | |
| Ensures interchangeability with schedulers that need to scale the denoising model input depending on the | |
| current timestep. | |
| 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 step( | |
| self, | |
| state: PNDMSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| return_dict: bool = True, | |
| ) -> Union[FlaxPNDMSchedulerOutput, 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: | |
| state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class | |
| Returns: | |
| [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] if `return_dict` is True, otherwise a | |
| `tuple`. When returning a tuple, the first element is the sample tensor. | |
| """ | |
| if self.config.skip_prk_steps: | |
| prev_sample, state = self.step_plms( | |
| state=state, model_output=model_output, timestep=timestep, sample=sample | |
| ) | |
| else: | |
| prev_sample, state = jax.lax.switch( | |
| jnp.where(state.counter < len(state.prk_timesteps), 0, 1), | |
| (self.step_prk, self.step_plms), | |
| # Args to either branch | |
| state, | |
| model_output, | |
| timestep, | |
| sample, | |
| ) | |
| if not return_dict: | |
| return (prev_sample, state) | |
| return FlaxPNDMSchedulerOutput(prev_sample=prev_sample, state=state) | |
| def step_prk( | |
| self, | |
| state: PNDMSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| ) -> Union[FlaxPNDMSchedulerOutput, 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: | |
| state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class | |
| Returns: | |
| [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] 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" | |
| ) | |
| diff_to_prev = jnp.where( | |
| state.counter % 2, 0, self.config.num_train_timesteps // state.num_inference_steps // 2 | |
| ) | |
| prev_timestep = timestep - diff_to_prev | |
| timestep = state.prk_timesteps[state.counter // 4 * 4] | |
| def remainder_0(state: PNDMSchedulerState, model_output: jnp.ndarray, ets_at: int): | |
| return ( | |
| state.replace( | |
| cur_model_output=state.cur_model_output + 1 / 6 * model_output, | |
| ets=state.ets.at[ets_at].set(model_output), | |
| cur_sample=sample, | |
| ), | |
| model_output, | |
| ) | |
| def remainder_1(state: PNDMSchedulerState, model_output: jnp.ndarray, ets_at: int): | |
| return state.replace(cur_model_output=state.cur_model_output + 1 / 3 * model_output), model_output | |
| def remainder_2(state: PNDMSchedulerState, model_output: jnp.ndarray, ets_at: int): | |
| return state.replace(cur_model_output=state.cur_model_output + 1 / 3 * model_output), model_output | |
| def remainder_3(state: PNDMSchedulerState, model_output: jnp.ndarray, ets_at: int): | |
| model_output = state.cur_model_output + 1 / 6 * model_output | |
| return state.replace(cur_model_output=jnp.zeros_like(state.cur_model_output)), model_output | |
| state, model_output = jax.lax.switch( | |
| state.counter % 4, | |
| (remainder_0, remainder_1, remainder_2, remainder_3), | |
| # Args to either branch | |
| state, | |
| model_output, | |
| state.counter // 4, | |
| ) | |
| cur_sample = state.cur_sample | |
| prev_sample = self._get_prev_sample(cur_sample, timestep, prev_timestep, model_output) | |
| state = state.replace(counter=state.counter + 1) | |
| return (prev_sample, state) | |
| def step_plms( | |
| self, | |
| state: PNDMSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| ) -> Union[FlaxPNDMSchedulerOutput, 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: | |
| state (`PNDMSchedulerState`): the `FlaxPNDMScheduler` 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 FlaxPNDMSchedulerOutput class | |
| Returns: | |
| [`FlaxPNDMSchedulerOutput`] or `tuple`: [`FlaxPNDMSchedulerOutput`] 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" | |
| ) | |
| if not self.config.skip_prk_steps and len(state.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 // state.num_inference_steps | |
| prev_timestep = jnp.where(prev_timestep > 0, prev_timestep, 0) | |
| # Reference: | |
| # if state.counter != 1: | |
| # state.ets.append(model_output) | |
| # else: | |
| # prev_timestep = timestep | |
| # timestep = timestep + self.config.num_train_timesteps // state.num_inference_steps | |
| prev_timestep = jnp.where(state.counter == 1, timestep, prev_timestep) | |
| timestep = jnp.where( | |
| state.counter == 1, timestep + self.config.num_train_timesteps // state.num_inference_steps, timestep | |
| ) | |
| # Reference: | |
| # if len(state.ets) == 1 and state.counter == 0: | |
| # model_output = model_output | |
| # state.cur_sample = sample | |
| # elif len(state.ets) == 1 and state.counter == 1: | |
| # model_output = (model_output + state.ets[-1]) / 2 | |
| # sample = state.cur_sample | |
| # state.cur_sample = None | |
| # elif len(state.ets) == 2: | |
| # model_output = (3 * state.ets[-1] - state.ets[-2]) / 2 | |
| # elif len(state.ets) == 3: | |
| # model_output = (23 * state.ets[-1] - 16 * state.ets[-2] + 5 * state.ets[-3]) / 12 | |
| # else: | |
| # model_output = (1 / 24) * (55 * state.ets[-1] - 59 * state.ets[-2] + 37 * state.ets[-3] - 9 * state.ets[-4]) | |
| def counter_0(state: PNDMSchedulerState): | |
| ets = state.ets.at[0].set(model_output) | |
| return state.replace( | |
| ets=ets, | |
| cur_sample=sample, | |
| cur_model_output=jnp.array(model_output, dtype=jnp.float32), | |
| ) | |
| def counter_1(state: PNDMSchedulerState): | |
| return state.replace( | |
| cur_model_output=(model_output + state.ets[0]) / 2, | |
| ) | |
| def counter_2(state: PNDMSchedulerState): | |
| ets = state.ets.at[1].set(model_output) | |
| return state.replace( | |
| ets=ets, | |
| cur_model_output=(3 * ets[1] - ets[0]) / 2, | |
| cur_sample=sample, | |
| ) | |
| def counter_3(state: PNDMSchedulerState): | |
| ets = state.ets.at[2].set(model_output) | |
| return state.replace( | |
| ets=ets, | |
| cur_model_output=(23 * ets[2] - 16 * ets[1] + 5 * ets[0]) / 12, | |
| cur_sample=sample, | |
| ) | |
| def counter_other(state: PNDMSchedulerState): | |
| ets = state.ets.at[3].set(model_output) | |
| next_model_output = (1 / 24) * (55 * ets[3] - 59 * ets[2] + 37 * ets[1] - 9 * ets[0]) | |
| ets = ets.at[0].set(ets[1]) | |
| ets = ets.at[1].set(ets[2]) | |
| ets = ets.at[2].set(ets[3]) | |
| return state.replace( | |
| ets=ets, | |
| cur_model_output=next_model_output, | |
| cur_sample=sample, | |
| ) | |
| counter = jnp.clip(state.counter, 0, 4) | |
| state = jax.lax.switch( | |
| counter, | |
| [counter_0, counter_1, counter_2, counter_3, counter_other], | |
| state, | |
| ) | |
| sample = state.cur_sample | |
| model_output = state.cur_model_output | |
| prev_sample = self._get_prev_sample(sample, timestep, prev_timestep, model_output) | |
| state = state.replace(counter=state.counter + 1) | |
| return (prev_sample, state) | |
| 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 = jnp.where(prev_timestep >= 0, self.alphas_cumprod[prev_timestep], self.final_alpha_cumprod) | |
| beta_prod_t = 1 - alpha_prod_t | |
| beta_prod_t_prev = 1 - alpha_prod_t_prev | |
| # 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: 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 | |