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# Copyright 2022 NVIDIA 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 jax import random
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin
@flax.struct.dataclass
class KarrasVeSchedulerState:
# setable values
num_inference_steps: Optional[int] = None
timesteps: Optional[jnp.ndarray] = None
schedule: Optional[jnp.ndarray] = None # sigma(t_i)
@classmethod
def create(cls):
return cls()
@dataclass
class FlaxKarrasVeOutput(BaseOutput):
"""
Output class for the scheduler's step function output.
Args:
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.
derivative (`jnp.ndarray` of shape `(batch_size, num_channels, height, width)` for images):
Derivative of predicted original image sample (x_0).
state (`KarrasVeSchedulerState`): the `FlaxKarrasVeScheduler` state data class.
"""
prev_sample: jnp.ndarray
derivative: jnp.ndarray
state: KarrasVeSchedulerState
class FlaxKarrasVeScheduler(FlaxSchedulerMixin, ConfigMixin):
"""
Stochastic sampling from Karras et al. [1] tailored to the Variance-Expanding (VE) models [2]. Use Algorithm 2 and
the VE column of Table 1 from [1] for reference.
[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
https://arxiv.org/abs/2206.00364 [2] Song, Yang, et al. "Score-based generative modeling through stochastic
differential equations." 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.
For more details on the parameters, see the original paper's Appendix E.: "Elucidating the Design Space of
Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364. The grid search values used to find the
optimal {s_noise, s_churn, s_min, s_max} for a specific model are described in Table 5 of the paper.
Args:
sigma_min (`float`): minimum noise magnitude
sigma_max (`float`): maximum noise magnitude
s_noise (`float`): the amount of additional noise to counteract loss of detail during sampling.
A reasonable range is [1.000, 1.011].
s_churn (`float`): the parameter controlling the overall amount of stochasticity.
A reasonable range is [0, 100].
s_min (`float`): the start value of the sigma range where we add noise (enable stochasticity).
A reasonable range is [0, 10].
s_max (`float`): the end value of the sigma range where we add noise.
A reasonable range is [0.2, 80].
"""
@property
def has_state(self):
return True
@register_to_config
def __init__(
self,
sigma_min: float = 0.02,
sigma_max: float = 100,
s_noise: float = 1.007,
s_churn: float = 80,
s_min: float = 0.05,
s_max: float = 50,
):
pass
def create_state(self):
return KarrasVeSchedulerState.create()
def set_timesteps(
self, state: KarrasVeSchedulerState, num_inference_steps: int, shape: Tuple = ()
) -> KarrasVeSchedulerState:
"""
Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
state (`KarrasVeSchedulerState`):
the `FlaxKarrasVeScheduler` state data class.
num_inference_steps (`int`):
the number of diffusion steps used when generating samples with a pre-trained model.
"""
timesteps = jnp.arange(0, num_inference_steps)[::-1].copy()
schedule = [
(
self.config.sigma_max**2
* (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
)
for i in timesteps
]
return state.replace(
num_inference_steps=num_inference_steps,
schedule=jnp.array(schedule, dtype=jnp.float32),
timesteps=timesteps,
)
def add_noise_to_input(
self,
state: KarrasVeSchedulerState,
sample: jnp.ndarray,
sigma: float,
key: random.KeyArray,
) -> Tuple[jnp.ndarray, float]:
"""
Explicit Langevin-like "churn" step of adding noise to the sample according to a factor gamma_i ≥ 0 to reach a
higher noise level sigma_hat = sigma_i + gamma_i*sigma_i.
TODO Args:
"""
if self.config.s_min <= sigma <= self.config.s_max:
gamma = min(self.config.s_churn / state.num_inference_steps, 2**0.5 - 1)
else:
gamma = 0
# sample eps ~ N(0, S_noise^2 * I)
key = random.split(key, num=1)
eps = self.config.s_noise * random.normal(key=key, shape=sample.shape)
sigma_hat = sigma + gamma * sigma
sample_hat = sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)
return sample_hat, sigma_hat
def step(
self,
state: KarrasVeSchedulerState,
model_output: jnp.ndarray,
sigma_hat: float,
sigma_prev: float,
sample_hat: jnp.ndarray,
return_dict: bool = True,
) -> Union[FlaxKarrasVeOutput, 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 (`KarrasVeSchedulerState`): the `FlaxKarrasVeScheduler` state data class.
model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
sigma_hat (`float`): TODO
sigma_prev (`float`): TODO
sample_hat (`torch.FloatTensor` or `np.ndarray`): TODO
return_dict (`bool`): option for returning tuple rather than FlaxKarrasVeOutput class
Returns:
[`~schedulers.scheduling_karras_ve_flax.FlaxKarrasVeOutput`] or `tuple`: Updated sample in the diffusion
chain and derivative. [`~schedulers.scheduling_karras_ve_flax.FlaxKarrasVeOutput`] if `return_dict` is
True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.
"""
pred_original_sample = sample_hat + sigma_hat * model_output
derivative = (sample_hat - pred_original_sample) / sigma_hat
sample_prev = sample_hat + (sigma_prev - sigma_hat) * derivative
if not return_dict:
return (sample_prev, derivative, state)
return FlaxKarrasVeOutput(prev_sample=sample_prev, derivative=derivative, state=state)
def step_correct(
self,
state: KarrasVeSchedulerState,
model_output: jnp.ndarray,
sigma_hat: float,
sigma_prev: float,
sample_hat: jnp.ndarray,
sample_prev: jnp.ndarray,
derivative: jnp.ndarray,
return_dict: bool = True,
) -> Union[FlaxKarrasVeOutput, Tuple]:
"""
Correct the predicted sample based on the output model_output of the network. TODO complete description
Args:
state (`KarrasVeSchedulerState`): the `FlaxKarrasVeScheduler` state data class.
model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
sigma_hat (`float`): TODO
sigma_prev (`float`): TODO
sample_hat (`torch.FloatTensor` or `np.ndarray`): TODO
sample_prev (`torch.FloatTensor` or `np.ndarray`): TODO
derivative (`torch.FloatTensor` or `np.ndarray`): TODO
return_dict (`bool`): option for returning tuple rather than FlaxKarrasVeOutput class
Returns:
prev_sample (TODO): updated sample in the diffusion chain. derivative (TODO): TODO
"""
pred_original_sample = sample_prev + sigma_prev * model_output
derivative_corr = (sample_prev - pred_original_sample) / sigma_prev
sample_prev = sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)
if not return_dict:
return (sample_prev, derivative, state)
return FlaxKarrasVeOutput(prev_sample=sample_prev, derivative=derivative, state=state)
def add_noise(self, original_samples, noise, timesteps):
raise NotImplementedError()
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