scheduling_ddpm_flax.py

# Copyright 2022 UC Berkeley Team and The HuggingFace Team. All rights reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#     http://www.apache.org/licenses/LICENSE-2.0
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# 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 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)


@flax.struct.dataclass
class DDPMSchedulerState:
    # setable values
    timesteps: jnp.ndarray
    num_inference_steps: Optional[int] = None

    @classmethod
    def create(cls, num_train_timesteps: int):
        return cls(timesteps=jnp.arange(0, num_train_timesteps)[::-1])


@dataclass
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`.
    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
    [`~ConfigMixin.from_config`] 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.
        predict_epsilon (`bool`):
            optional flag to use when the model predicts the noise (epsilon), or the samples instead of the noise.

    """

    @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,
        variance_type: str = "fixed_small",
        clip_sample: bool = True,
        predict_epsilon: bool = True,
    ):
        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,
        predict_epsilon: bool = True,
        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 `predict_epsilon` instead. E.g. `scheduler ="
            " DDPMScheduler.from_config(<model_id>, predict_epsilon=True)`."
        )
        predict_epsilon = deprecate("predict_epsilon", "0.10.0", message, take_from=kwargs)
        if predict_epsilon is not None and predict_epsilon != self.config.predict_epsilon:
            new_config = dict(self.config)
            new_config["predict_epsilon"] = predict_epsilon
            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.predict_epsilon:
            pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
        else:
            pred_original_sample = model_output

        # 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