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# 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
#
# 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.
# 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
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