scheduling_ddim_flax.py

# 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
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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

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 (<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"

        # 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)
        elif self.config.prediction_type == "sample":
            pred_original_sample = model_output
        elif self.config.prediction_type == "v_prediction":
            pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
            # predict V
            model_output = (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) * 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 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