scheduling_ddim_flax.py

# Copyright 2022 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
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#     http://www.apache.org/licenses/LICENSE-2.0
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# 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.
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# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

import math
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 import SchedulerMixin, SchedulerOutput


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 DDIMSchedulerState:
    # setable values
    timesteps: jnp.ndarray
    alphas_cumprod: jnp.ndarray
    num_inference_steps: Optional[int] = None

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


@dataclass
class FlaxSchedulerOutput(SchedulerOutput):
    state: DDIMSchedulerState


class FlaxDDIMScheduler(SchedulerMixin, 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`.
    [`~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/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.
    """

    @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",
        set_alpha_to_one: bool = True,
        steps_offset: int = 0,
    ):
        if 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

        # HACK for now - clean up later (PVP)
        self._alphas_cumprod = jnp.cumprod(self.alphas, axis=0)

        # 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.
        self.final_alpha_cumprod = jnp.array(1.0) if set_alpha_to_one else float(self._alphas_cumprod[0])

    def create_state(self):
        return DDIMSchedulerState.create(
            num_train_timesteps=self.config.num_train_timesteps, alphas_cumprod=self._alphas_cumprod
        )

    def _get_variance(self, timestep, prev_timestep, alphas_cumprod):
        alpha_prod_t = alphas_cumprod[timestep]
        alpha_prod_t_prev = jnp.where(prev_timestep >= 0, alphas_cumprod[prev_timestep], self.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 set_timesteps(self, state: DDIMSchedulerState, num_inference_steps: int) -> 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.
        """
        offset = self.config.steps_offset

        step_ratio = self.config.num_train_timesteps // num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # casting to int to avoid issues when num_inference_step is power of 3
        timesteps = (jnp.arange(0, num_inference_steps) * step_ratio).round()[::-1]
        timesteps = timesteps + offset

        return state.replace(num_inference_steps=num_inference_steps, timesteps=timesteps)

    def step(
        self,
        state: DDIMSchedulerState,
        model_output: jnp.ndarray,
        timestep: int,
        sample: jnp.ndarray,
        return_dict: bool = True,
    ) -> Union[FlaxSchedulerOutput, 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.
            key (`random.KeyArray`): a PRNG key.
            eta (`float`): weight of noise for added noise in diffusion step.
            use_clipped_model_output (`bool`): TODO
            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class

        Returns:
            [`FlaxSchedulerOutput`] or `tuple`: [`FlaxSchedulerOutput`] 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 (<variable name> -> <name in paper>
        # - 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"

        # TODO(Patrick) - eta is always 0.0 for now, allow to be set in step function
        eta = 0.0

        # 1. get previous step value (=t-1)
        prev_timestep = timestep - self.config.num_train_timesteps // state.num_inference_steps

        alphas_cumprod = state.alphas_cumprod

        # 2. compute alphas, betas
        alpha_prod_t = alphas_cumprod[timestep]
        alpha_prod_t_prev = jnp.where(prev_timestep >= 0, alphas_cumprod[prev_timestep], self.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
        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)

        # 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(timestep, prev_timestep, alphas_cumprod)
        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) * model_output

        # 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 FlaxSchedulerOutput(prev_sample=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()
        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
            sqrt_alpha_prod = sqrt_alpha_prod[:, None]

        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.0
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod[:, None]

        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