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| # Copyright 2022 Katherine Crowson 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. | |
| from dataclasses import dataclass | |
| from typing import Optional, Tuple, Union | |
| import flax | |
| import jax.numpy as jnp | |
| from scipy import integrate | |
| 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, | |
| ) | |
| class LMSDiscreteSchedulerState: | |
| # setable values | |
| num_inference_steps: Optional[int] = None | |
| timesteps: Optional[jnp.ndarray] = None | |
| sigmas: Optional[jnp.ndarray] = None | |
| derivatives: jnp.ndarray = jnp.array([]) | |
| def create(cls, num_train_timesteps: int, sigmas: jnp.ndarray): | |
| return cls(timesteps=jnp.arange(0, num_train_timesteps)[::-1], sigmas=sigmas) | |
| class FlaxLMSSchedulerOutput(FlaxSchedulerOutput): | |
| state: LMSDiscreteSchedulerState | |
| class FlaxLMSDiscreteScheduler(FlaxSchedulerMixin, ConfigMixin): | |
| """ | |
| Linear Multistep Scheduler for discrete beta schedules. Based on the original k-diffusion implementation by | |
| Katherine Crowson: | |
| https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L181 | |
| [`~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. | |
| 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` or `scaled_linear`. | |
| trained_betas (`jnp.ndarray`, optional): | |
| option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc. | |
| """ | |
| _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, | |
| ): | |
| 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 | |
| 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) | |
| def create_state(self): | |
| self.state = LMSDiscreteSchedulerState.create( | |
| num_train_timesteps=self.config.num_train_timesteps, | |
| sigmas=((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5, | |
| ) | |
| def scale_model_input(self, state: LMSDiscreteSchedulerState, sample: jnp.ndarray, timestep: int) -> jnp.ndarray: | |
| """ | |
| Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm. | |
| Args: | |
| state (`LMSDiscreteSchedulerState`): | |
| the `FlaxLMSDiscreteScheduler` state data class instance. | |
| sample (`jnp.ndarray`): | |
| current instance of sample being created by diffusion process. | |
| timestep (`int`): | |
| current discrete timestep in the diffusion chain. | |
| Returns: | |
| `jnp.ndarray`: scaled input sample | |
| """ | |
| (step_index,) = jnp.where(state.timesteps == timestep, size=1) | |
| sigma = state.sigmas[step_index] | |
| sample = sample / ((sigma**2 + 1) ** 0.5) | |
| return sample | |
| def get_lms_coefficient(self, state, order, t, current_order): | |
| """ | |
| Compute a linear multistep coefficient. | |
| Args: | |
| order (TODO): | |
| t (TODO): | |
| current_order (TODO): | |
| """ | |
| def lms_derivative(tau): | |
| prod = 1.0 | |
| for k in range(order): | |
| if current_order == k: | |
| continue | |
| prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k]) | |
| return prod | |
| integrated_coeff = integrate.quad(lms_derivative, state.sigmas[t], state.sigmas[t + 1], epsrel=1e-4)[0] | |
| return integrated_coeff | |
| def set_timesteps( | |
| self, state: LMSDiscreteSchedulerState, num_inference_steps: int, shape: Tuple = () | |
| ) -> LMSDiscreteSchedulerState: | |
| """ | |
| Sets the timesteps used for the diffusion chain. Supporting function to be run before inference. | |
| Args: | |
| state (`LMSDiscreteSchedulerState`): | |
| the `FlaxLMSDiscreteScheduler` state data class instance. | |
| num_inference_steps (`int`): | |
| the number of diffusion steps used when generating samples with a pre-trained model. | |
| """ | |
| timesteps = jnp.linspace(self.config.num_train_timesteps - 1, 0, num_inference_steps, dtype=jnp.float32) | |
| low_idx = jnp.floor(timesteps).astype(int) | |
| high_idx = jnp.ceil(timesteps).astype(int) | |
| frac = jnp.mod(timesteps, 1.0) | |
| sigmas = jnp.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
| sigmas = (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx] | |
| sigmas = jnp.concatenate([sigmas, jnp.array([0.0])]).astype(jnp.float32) | |
| return state.replace( | |
| num_inference_steps=num_inference_steps, | |
| timesteps=timesteps.astype(int), | |
| derivatives=jnp.array([]), | |
| sigmas=sigmas, | |
| ) | |
| def step( | |
| self, | |
| state: LMSDiscreteSchedulerState, | |
| model_output: jnp.ndarray, | |
| timestep: int, | |
| sample: jnp.ndarray, | |
| order: int = 4, | |
| return_dict: bool = True, | |
| ) -> Union[FlaxLMSSchedulerOutput, 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 (`LMSDiscreteSchedulerState`): the `FlaxLMSDiscreteScheduler` 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. | |
| order: coefficient for multi-step inference. | |
| return_dict (`bool`): option for returning tuple rather than FlaxLMSSchedulerOutput class | |
| Returns: | |
| [`FlaxLMSSchedulerOutput`] or `tuple`: [`FlaxLMSSchedulerOutput`] if `return_dict` is True, otherwise a | |
| `tuple`. When returning a tuple, the first element is the sample tensor. | |
| """ | |
| sigma = state.sigmas[timestep] | |
| # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise | |
| pred_original_sample = sample - sigma * model_output | |
| # 2. Convert to an ODE derivative | |
| derivative = (sample - pred_original_sample) / sigma | |
| state = state.replace(derivatives=jnp.append(state.derivatives, derivative)) | |
| if len(state.derivatives) > order: | |
| state = state.replace(derivatives=jnp.delete(state.derivatives, 0)) | |
| # 3. Compute linear multistep coefficients | |
| order = min(timestep + 1, order) | |
| lms_coeffs = [self.get_lms_coefficient(state, order, timestep, curr_order) for curr_order in range(order)] | |
| # 4. Compute previous sample based on the derivatives path | |
| prev_sample = sample + sum( | |
| coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(state.derivatives)) | |
| ) | |
| if not return_dict: | |
| return (prev_sample, state) | |
| return FlaxLMSSchedulerOutput(prev_sample=prev_sample, state=state) | |
| def add_noise( | |
| self, | |
| state: LMSDiscreteSchedulerState, | |
| original_samples: jnp.ndarray, | |
| noise: jnp.ndarray, | |
| timesteps: jnp.ndarray, | |
| ) -> jnp.ndarray: | |
| sigma = state.sigmas[timesteps].flatten() | |
| sigma = broadcast_to_shape_from_left(sigma, noise.shape) | |
| noisy_samples = original_samples + noise * sigma | |
| return noisy_samples | |
| def __len__(self): | |
| return self.config.num_train_timesteps | |