# Copyright 2024 Google Brain and The HuggingFace Team. All rights reserved.
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# Licensed under the Apache License, Version 2.0 (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/yang-song/score_sde_pytorch
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import flax
import jax
import jax.numpy as jnp
from jax import random
from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left
@flax.struct.dataclass
class ScoreSdeVeSchedulerState:
# setable values
timesteps: Optional[jnp.ndarray] = None
discrete_sigmas: Optional[jnp.ndarray] = None
sigmas: Optional[jnp.ndarray] = None
@classmethod
def create(cls):
return cls()
@dataclass
class FlaxSdeVeOutput(FlaxSchedulerOutput):
"""
Output class for the ScoreSdeVeScheduler's step function output.
Args:
state (`ScoreSdeVeSchedulerState`):
prev_sample (`jnp.ndarray` of shape `(batch_size, num_channels, height, width)` for images):
Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the
denoising loop.
prev_sample_mean (`jnp.ndarray` of shape `(batch_size, num_channels, height, width)` for images):
Mean averaged `prev_sample`. Same as `prev_sample`, only mean-averaged over previous timesteps.
"""
state: ScoreSdeVeSchedulerState
prev_sample: jnp.ndarray
prev_sample_mean: Optional[jnp.ndarray] = None
class FlaxScoreSdeVeScheduler(FlaxSchedulerMixin, ConfigMixin):
"""
The variance exploding stochastic differential equation (SDE) scheduler.
For more information, see the original paper: https://arxiv.org/abs/2011.13456
[`~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.
snr (`float`):
coefficient weighting the step from the model_output sample (from the network) to the random noise.
sigma_min (`float`):
initial noise scale for sigma sequence in sampling procedure. The minimum sigma should mirror the
distribution of the data.
sigma_max (`float`): maximum value used for the range of continuous timesteps passed into the model.
sampling_eps (`float`): the end value of sampling, where timesteps decrease progressively from 1 to
epsilon.
correct_steps (`int`): number of correction steps performed on a produced sample.
"""
@property
def has_state(self):
return True
@register_to_config
def __init__(
self,
num_train_timesteps: int = 2000,
snr: float = 0.15,
sigma_min: float = 0.01,
sigma_max: float = 1348.0,
sampling_eps: float = 1e-5,
correct_steps: int = 1,
):
pass
def create_state(self):
state = ScoreSdeVeSchedulerState.create()
return self.set_sigmas(
state,
self.config.num_train_timesteps,
self.config.sigma_min,
self.config.sigma_max,
self.config.sampling_eps,
)
def set_timesteps(
self, state: ScoreSdeVeSchedulerState, num_inference_steps: int, shape: Tuple = (), sampling_eps: float = None
) -> ScoreSdeVeSchedulerState:
"""
Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance.
num_inference_steps (`int`):
the number of diffusion steps used when generating samples with a pre-trained model.
sampling_eps (`float`, optional):
final timestep value (overrides value given at Scheduler instantiation).
"""
sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
timesteps = jnp.linspace(1, sampling_eps, num_inference_steps)
return state.replace(timesteps=timesteps)
def set_sigmas(
self,
state: ScoreSdeVeSchedulerState,
num_inference_steps: int,
sigma_min: float = None,
sigma_max: float = None,
sampling_eps: float = None,
) -> ScoreSdeVeSchedulerState:
"""
Sets the noise scales used for the diffusion chain. Supporting function to be run before inference.
The sigmas control the weight of the `drift` and `diffusion` components of sample update.
Args:
state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance.
num_inference_steps (`int`):
the number of diffusion steps used when generating samples with a pre-trained model.
sigma_min (`float`, optional):
initial noise scale value (overrides value given at Scheduler instantiation).
sigma_max (`float`, optional):
final noise scale value (overrides value given at Scheduler instantiation).
sampling_eps (`float`, optional):
final timestep value (overrides value given at Scheduler instantiation).
"""
sigma_min = sigma_min if sigma_min is not None else self.config.sigma_min
sigma_max = sigma_max if sigma_max is not None else self.config.sigma_max
sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
if state.timesteps is None:
state = self.set_timesteps(state, num_inference_steps, sampling_eps)
discrete_sigmas = jnp.exp(jnp.linspace(jnp.log(sigma_min), jnp.log(sigma_max), num_inference_steps))
sigmas = jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps])
return state.replace(discrete_sigmas=discrete_sigmas, sigmas=sigmas)
def get_adjacent_sigma(self, state, timesteps, t):
return jnp.where(timesteps == 0, jnp.zeros_like(t), state.discrete_sigmas[timesteps - 1])
def step_pred(
self,
state: ScoreSdeVeSchedulerState,
model_output: jnp.ndarray,
timestep: int,
sample: jnp.ndarray,
key: jax.Array,
return_dict: bool = True,
) -> Union[FlaxSdeVeOutput, 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 (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` 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.
generator: random number generator.
return_dict (`bool`): option for returning tuple rather than FlaxSdeVeOutput class
Returns:
[`FlaxSdeVeOutput`] or `tuple`: [`FlaxSdeVeOutput`] if `return_dict` is True, otherwise a `tuple`. When
returning a tuple, the first element is the sample tensor.
"""
if state.timesteps is None:
raise ValueError(
"`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"
)
timestep = timestep * jnp.ones(
sample.shape[0],
)
timesteps = (timestep * (len(state.timesteps) - 1)).long()
sigma = state.discrete_sigmas[timesteps]
adjacent_sigma = self.get_adjacent_sigma(state, timesteps, timestep)
drift = jnp.zeros_like(sample)
diffusion = (sigma**2 - adjacent_sigma**2) ** 0.5
# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
# also equation 47 shows the analog from SDE models to ancestral sampling methods
diffusion = diffusion.flatten()
diffusion = broadcast_to_shape_from_left(diffusion, sample.shape)
drift = drift - diffusion**2 * model_output
# equation 6: sample noise for the diffusion term of
key = random.split(key, num=1)
noise = random.normal(key=key, shape=sample.shape)
prev_sample_mean = sample - drift # subtract because `dt` is a small negative timestep
# TODO is the variable diffusion the correct scaling term for the noise?
prev_sample = prev_sample_mean + diffusion * noise # add impact of diffusion field g
if not return_dict:
return (prev_sample, prev_sample_mean, state)
return FlaxSdeVeOutput(prev_sample=prev_sample, prev_sample_mean=prev_sample_mean, state=state)
def step_correct(
self,
state: ScoreSdeVeSchedulerState,
model_output: jnp.ndarray,
sample: jnp.ndarray,
key: jax.Array,
return_dict: bool = True,
) -> Union[FlaxSdeVeOutput, Tuple]:
"""
Correct the predicted sample based on the output model_output of the network. This is often run repeatedly
after making the prediction for the previous timestep.
Args:
state (`ScoreSdeVeSchedulerState`): the `FlaxScoreSdeVeScheduler` state data class instance.
model_output (`jnp.ndarray`): direct output from learned diffusion model.
sample (`jnp.ndarray`):
current instance of sample being created by diffusion process.
generator: random number generator.
return_dict (`bool`): option for returning tuple rather than FlaxSdeVeOutput class
Returns:
[`FlaxSdeVeOutput`] or `tuple`: [`FlaxSdeVeOutput`] if `return_dict` is True, otherwise a `tuple`. When
returning a tuple, the first element is the sample tensor.
"""
if state.timesteps is None:
raise ValueError(
"`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"
)
# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
# sample noise for correction
key = random.split(key, num=1)
noise = random.normal(key=key, shape=sample.shape)
# compute step size from the model_output, the noise, and the snr
grad_norm = jnp.linalg.norm(model_output)
noise_norm = jnp.linalg.norm(noise)
step_size = (self.config.snr * noise_norm / grad_norm) ** 2 * 2
step_size = step_size * jnp.ones(sample.shape[0])
# compute corrected sample: model_output term and noise term
step_size = step_size.flatten()
step_size = broadcast_to_shape_from_left(step_size, sample.shape)
prev_sample_mean = sample + step_size * model_output
prev_sample = prev_sample_mean + ((step_size * 2) ** 0.5) * noise
if not return_dict:
return (prev_sample, state)
return FlaxSdeVeOutput(prev_sample=prev_sample, state=state)
def __len__(self):
return self.config.num_train_timesteps