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# Copyright 2023 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 ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
CommonSchedulerState,
FlaxKarrasDiffusionSchedulers,
FlaxSchedulerMixin,
FlaxSchedulerOutput,
broadcast_to_shape_from_left,
)
@flax.struct.dataclass
class EulerDiscreteSchedulerState:
common: CommonSchedulerState
# setable values
init_noise_sigma: jnp.ndarray
timesteps: jnp.ndarray
sigmas: jnp.ndarray
num_inference_steps: Optional[int] = None
@classmethod
def create(
cls, common: CommonSchedulerState, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, sigmas: jnp.ndarray
):
return cls(common=common, init_noise_sigma=init_noise_sigma, timesteps=timesteps, sigmas=sigmas)
@dataclass
class FlaxEulerDiscreteSchedulerOutput(FlaxSchedulerOutput):
state: EulerDiscreteSchedulerState
class FlaxEulerDiscreteScheduler(FlaxSchedulerMixin, ConfigMixin):
"""
Euler scheduler (Algorithm 2) from Karras et al. (2022) https://arxiv.org/abs/2206.00364. . Based on the original
k-diffusion implementation by Katherine Crowson:
https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L51
[`~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.
prediction_type (`str`, default `epsilon`, optional):
prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
https://imagen.research.google/video/paper.pdf)
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,
prediction_type: str = "epsilon",
timestep_spacing: str = "linspace",
dtype: jnp.dtype = jnp.float32,
):
self.dtype = dtype
def create_state(self, common: Optional[CommonSchedulerState] = None) -> EulerDiscreteSchedulerState:
if common is None:
common = CommonSchedulerState.create(self)
timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1]
sigmas = ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5
sigmas = jnp.interp(timesteps, jnp.arange(0, len(sigmas)), sigmas)
sigmas = jnp.concatenate([sigmas, jnp.array([0.0], dtype=self.dtype)])
# standard deviation of the initial noise distribution
if self.config.timestep_spacing in ["linspace", "trailing"]:
init_noise_sigma = sigmas.max()
else:
init_noise_sigma = (sigmas.max() ** 2 + 1) ** 0.5
return EulerDiscreteSchedulerState.create(
common=common,
init_noise_sigma=init_noise_sigma,
timesteps=timesteps,
sigmas=sigmas,
)
def scale_model_input(self, state: EulerDiscreteSchedulerState, sample: jnp.ndarray, timestep: int) -> jnp.ndarray:
"""
Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
Args:
state (`EulerDiscreteSchedulerState`):
the `FlaxEulerDiscreteScheduler` 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)
step_index = step_index[0]
sigma = state.sigmas[step_index]
sample = sample / ((sigma**2 + 1) ** 0.5)
return sample
def set_timesteps(
self, state: EulerDiscreteSchedulerState, num_inference_steps: int, shape: Tuple = ()
) -> EulerDiscreteSchedulerState:
"""
Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
state (`EulerDiscreteSchedulerState`):
the `FlaxEulerDiscreteScheduler` state data class instance.
num_inference_steps (`int`):
the number of diffusion steps used when generating samples with a pre-trained model.
"""
if self.config.timestep_spacing == "linspace":
timesteps = jnp.linspace(self.config.num_train_timesteps - 1, 0, num_inference_steps, dtype=self.dtype)
elif self.config.timestep_spacing == "leading":
step_ratio = self.config.num_train_timesteps // num_inference_steps
timesteps = (jnp.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(float)
timesteps += 1
else:
raise ValueError(
f"timestep_spacing must be one of ['linspace', 'leading'], got {self.config.timestep_spacing}"
)
sigmas = ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
sigmas = jnp.interp(timesteps, jnp.arange(0, len(sigmas)), sigmas)
sigmas = jnp.concatenate([sigmas, jnp.array([0.0], dtype=self.dtype)])
# standard deviation of the initial noise distribution
if self.config.timestep_spacing in ["linspace", "trailing"]:
init_noise_sigma = sigmas.max()
else:
init_noise_sigma = (sigmas.max() ** 2 + 1) ** 0.5
return state.replace(
timesteps=timesteps,
sigmas=sigmas,
num_inference_steps=num_inference_steps,
init_noise_sigma=init_noise_sigma,
)
def step(
self,
state: EulerDiscreteSchedulerState,
model_output: jnp.ndarray,
timestep: int,
sample: jnp.ndarray,
return_dict: bool = True,
) -> Union[FlaxEulerDiscreteSchedulerOutput, 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 (`EulerDiscreteSchedulerState`):
the `FlaxEulerDiscreteScheduler` 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 FlaxEulerDiscreteScheduler class
Returns:
[`FlaxEulerDiscreteScheduler`] or `tuple`: [`FlaxEulerDiscreteScheduler`] 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"
)
(step_index,) = jnp.where(state.timesteps == timestep, size=1)
step_index = step_index[0]
sigma = state.sigmas[step_index]
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
if self.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma * model_output
elif self.config.prediction_type == "v_prediction":
# * c_out + input * c_skip
pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
# 2. Convert to an ODE derivative
derivative = (sample - pred_original_sample) / sigma
# dt = sigma_down - sigma
dt = state.sigmas[step_index + 1] - sigma
prev_sample = sample + derivative * dt
if not return_dict:
return (prev_sample, state)
return FlaxEulerDiscreteSchedulerOutput(prev_sample=prev_sample, state=state)
def add_noise(
self,
state: EulerDiscreteSchedulerState,
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
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