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1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 | # 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.
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from scipy.io import loadmat
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
from diffusers.utils import BaseOutput, is_scipy_available, logging
from pathlib import Path
@dataclass
class STORKSchedulerOutput(BaseOutput):
"""
Output class for the scheduler's `step` function output.
Args:
prev_sample (`torch.FloatTensor` 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: torch.FloatTensor
current_file = Path(__file__)
CONSTANTSFOLDER = f"{current_file.parent}/STORK_constants"
class STORKScheduler(SchedulerMixin, ConfigMixin):
"""
`STORKScheduler` uses modified stabilized Runge-Kutta method for the backward ODE in the diffusion or flow matching models.
This include the original STORK method and the modified STORK++ methods.
This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
methods the library implements for all schedulers such as loading and saving.
Args:
num_train_timesteps (`int`, defaults to 1000):
The number of diffusion steps to train the model.
shift (`float`, defaults to 1.0):
The shift value for the timestep schedule.
use_dynamic_shifting (`bool`, defaults to False):
Whether to apply timestep shifting on-the-fly based on the image resolution.
base_shift (`float`, defaults to 0.5):
Value to stabilize image generation. Increasing `base_shift` reduces variation and image is more consistent
with desired output.
max_shift (`float`, defaults to 1.15):
Value change allowed to latent vectors. Increasing `max_shift` encourages more variation and image may be
more exaggerated or stylized.
base_image_seq_len (`int`, defaults to 256):
The base image sequence length.
max_image_seq_len (`int`, defaults to 4096):
The maximum image sequence length.
invert_sigmas (`bool`, defaults to False):
Whether to invert the sigmas.
shift_terminal (`float`, defaults to None):
The end value of the shifted timestep schedule.
use_karras_sigmas (`bool`, defaults to False):
Whether to use Karras sigmas for step sizes in the noise schedule during sampling.
use_exponential_sigmas (`bool`, defaults to False):
Whether to use exponential sigmas for step sizes in the noise schedule during sampling.
use_beta_sigmas (`bool`, defaults to False):
Whether to use beta sigmas for step sizes in the noise schedule during sampling.
solver_order (`int`, defaults to 2):
The STORK order which can be `2` or `4`. It is recommended to use `solver_order=2` uniformly.
prediction_type (`str`, defaults to `epsilon`, *optional*):
Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process) or `flow_prediction`.
time_shift_type (`str`, defaults to "exponential"):
The type of dynamic resolution-dependent timestep shifting to apply. Either "exponential" or "linear".
derivative_order (`int`, defaults to 1):
The order of the Taylor expansion derivative to use for the sub-step velocity approximation. Only supports 1, 2 or 3.
s (`int`, defaults to 50):
The number of sub-steps to use in the STORK.
precision (`str`, defaults to "float32"):
The precision to use for the scheduler; supports "float32", "bfloat16", or "float16".
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
order = 1
@register_to_config
def __init__(
self,
num_train_timesteps: int = 1000,
shift: float = 1.0,
use_dynamic_shifting: bool = False,
beta_start: float = 0.0001,
beta_end: float = 0.02,
beta_schedule: str = "linear",
trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
stopping_eps: float = 1e-2,
solver_order: int = 4,
prediction_type: str = "epsilon",
time_shift_type: str = "exponential",
derivative_order: int = 1,
s: int = 50,
base_shift: Optional[float] = 0.5,
max_shift: Optional[float] = 1.15,
base_image_seq_len: Optional[int] = 256,
max_image_seq_len: Optional[int] = 4096,
invert_sigmas: bool = False,
shift_terminal: Optional[float] = None,
use_karras_sigmas: Optional[bool] = False,
use_exponential_sigmas: Optional[bool] = False,
use_beta_sigmas: Optional[bool] = False,
):
super().__init__()
# if prediction_type == "flow_prediction" and sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
# raise ValueError(
# "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
# )
if time_shift_type not in {"exponential", "linear"}:
raise ValueError("`time_shift_type` must either be 'exponential' or 'linear'.")
# We manually enforce precision to float32 for numerical issues.Add commentMore actions
self.np_dtype = np.float32
self.dtype = torch.float32
timesteps = np.linspace(1, num_train_timesteps, num_train_timesteps, dtype=self.np_dtype)[::-1].copy()
timesteps = torch.from_numpy(timesteps).to(dtype=self.dtype)
sigmas = timesteps / num_train_timesteps
if not use_dynamic_shifting:
# when use_dynamic_shifting is True, we apply the timestep shifting on the fly based on the image resolution
sigmas = shift * sigmas / (1 + (shift - 1) * sigmas)
self.timesteps = None #sigmas * num_train_timesteps
self._step_index = None
self._begin_index = None
self._shift = shift
self.sigmas = sigmas #.to("cpu") # to avoid too much CPU/GPU communication
self.sigma_min = self.sigmas[-1].item()
self.sigma_max = self.sigmas[0].item()
# Store the predictions for the velocity/noise for higher order derivative approximations
self.velocity_predictions = []
self.noise_predictions = []
self.s = s
self.derivative_order = derivative_order
self.solver_order = solver_order
self.prediction_type = prediction_type
# Set the betas for noise-based models
if trained_betas is not None:
self.betas = torch.tensor(trained_betas, dtype=torch.float32)
elif beta_schedule == "linear":
self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
elif beta_schedule == "scaled_linear":
# this schedule is very specific to the latent diffusion model.
self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
else:
raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
self.alphas = 1.0 - self.betas
self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
# standard deviation of the initial noise distribution
self.init_noise_sigma = 1.0
# Noise-based models epsilon to avoid numerical issues
self.stopping_eps = stopping_eps
def set_timesteps(
self,
num_inference_steps: Optional[int] = None,
device: Union[str, torch.device] = None,
sigmas: Optional[List[float]] = None,
mu: Optional[float] = None,
timesteps: Optional[List[float]] = None,
):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
num_inference_steps (`int`, *optional*):
The number of diffusion steps used when generating samples with a pre-trained model.
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
sigmas (`List[float]`, *optional*):
Custom values for sigmas to be used for each diffusion step. If `None`, the sigmas are computed
automatically.
mu (`float`, *optional*):
Determines the amount of shifting applied to sigmas when performing resolution-dependent timestep
shifting.
timesteps (`List[float]`, *optional*):
Custom values for timesteps to be used for each diffusion step. If `None`, the timesteps are computed
automatically.
"""
if self.config.use_dynamic_shifting and mu is None:
raise ValueError("`mu` must be passed when `use_dynamic_shifting` is set to be `True`")
if sigmas is not None and timesteps is not None:
if len(sigmas) != len(timesteps):
raise ValueError("`sigmas` and `timesteps` should have the same length")
if num_inference_steps is not None:
if (sigmas is not None and len(sigmas) != num_inference_steps) or (
timesteps is not None and len(timesteps) != num_inference_steps
):
raise ValueError(
"`sigmas` and `timesteps` should have the same length as num_inference_steps, if `num_inference_steps` is provided"
)
else:
num_inference_steps = len(sigmas) if sigmas is not None else len(timesteps)
self.num_inference_steps = num_inference_steps
if self.prediction_type == "epsilon":
self.set_timesteps_noise(num_inference_steps, device)
elif self.prediction_type == "flow_prediction":
self.set_timesteps_flow_matching(num_inference_steps, device, sigmas, mu, timesteps)
else:
raise ValueError(f"Prediction type {self.prediction_type} is not yet supported")
# Reset the step index and begin index
self._step_index = None
self._begin_index = None
def set_timesteps_noise(self,
num_inference_steps: Optional[int] = None,
device: Union[str, torch.device] = None,
):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference), for noise-based models.
Args:
num_inference_steps (`int`, *optional*):
The number of diffusion steps used when generating samples with a pre-trained model.
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
"""
seq = np.linspace(0, 1, self.num_inference_steps+1)
seq[0] = self.stopping_eps
seq = seq[:-1]
seq = seq[::-1]
# The following lines are for the uniform timestepping case
self.dt = seq[0] - seq[1]
seq = seq * self.config.num_train_timesteps
seq[-1] = self.stopping_eps * self.config.num_train_timesteps
self._timesteps = seq
self.timesteps = torch.from_numpy(seq.copy()).to(device)
self._step_index = None
self._begin_index = None
self.noise_predictions = []
def set_timesteps_flow_matching(self,
num_inference_steps: Optional[int] = None,
device: Union[str, torch.device] = None,
sigmas: Optional[List[float]] = None,
mu: Optional[float] = None,
timesteps: Optional[List[float]] = None,
):
"""
Sets the discrete timesteps used for the flow matching based models (to be run before inference).
Args:
num_inference_steps (`int`, *optional*):
The number of diffusion steps used when generating samples with a pre-trained model.
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
sigmas (`List[float]`, *optional*):
Custom values for sigmas to be used for each diffusion step. If `None`, the sigmas are computed
automatically.
mu (`float`, *optional*):
Determines the amount of shifting applied to sigmas when performing resolution-dependent timestep
shifting.
timesteps (`List[float]`, *optional*):
Custom values for timesteps to be used for each diffusion step. If `None`, the timesteps are computed
automatically.
"""
self.num_inference_steps = num_inference_steps
# 1. Prepare default sigmas
is_timesteps_provided = timesteps is not None
if is_timesteps_provided:
timesteps = np.array(timesteps).astype(np.float32)
if sigmas is None:
if timesteps is None:
timesteps = np.linspace(
self._sigma_to_t(self.sigma_max), self._sigma_to_t(self.sigma_min), num_inference_steps
)
sigmas = timesteps / self.config.num_train_timesteps
else:
sigmas = np.array(sigmas).astype(np.float32)
num_inference_steps = len(sigmas)
# 2. Perform timestep shifting. Either no shifting is applied, or resolution-dependent shifting of
# "exponential" or "linear" type is applied
if self.config.use_dynamic_shifting:
sigmas = self.time_shift(mu, 1.0, sigmas)
else:
sigmas = self.shift * sigmas / (1 + (self.shift - 1) * sigmas)
# 3. If required, stretch the sigmas schedule to terminate at the configured `shift_terminal` value
if self.config.shift_terminal:
sigmas = self.stretch_shift_to_terminal(sigmas)
# 4. If required, convert sigmas to one of karras, exponential, or beta sigma schedules
if self.config.use_karras_sigmas:
sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
elif self.config.use_exponential_sigmas:
sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
elif self.config.use_beta_sigmas:
sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
# 5. Convert sigmas and timesteps to tensors and move to specified device
sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32, device=device)
if not is_timesteps_provided:
timesteps = sigmas * self.config.num_train_timesteps
else:
timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32, device=device)
# 6. Append the terminal sigma value.
# If a model requires inverted sigma schedule for denoising but timesteps without inversion, the
# `invert_sigmas` flag can be set to `True`. This case is only required in Mochi
if self.config.invert_sigmas:
sigmas = 1.0 - sigmas
timesteps = sigmas * self.config.num_train_timesteps
sigmas = torch.cat([sigmas, torch.ones(1, device=sigmas.device)])
else:
sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])
self.timesteps = timesteps
self.sigmas = sigmas
# Create the dt list
self.dt_list = self.sigmas[:-1] - self.sigmas[1:]
self.dt_list = self.dt_list.reshape(-1)
self.dt_list = self.dt_list.tolist()
self.dt_list = torch.tensor(self.dt_list).to(self.dtype)
self.velocity_predictions = []
@property
def shift(self):
"""
The value used for shifting.
"""
return self._shift
@property
def step_index(self):
"""
The index counter for current timestep. It will increase 1 after each scheduler step.
"""
return self._step_index
@property
def begin_index(self):
"""
The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
"""
return self._begin_index
def set_shift(self, shift: float):
self._shift = shift
def set_begin_index(self, begin_index: int):
"""
Set the begin index for the scheduler.
Args:
begin_index (`int`):
The begin index to set.
"""
self._begin_index = begin_index
def scale_noise(
self,
sample: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
noise: Optional[torch.FloatTensor] = None,
) -> torch.FloatTensor:
"""
Forward process in flow-matching
Args:
sample (`torch.FloatTensor`):
The input sample.
timestep (`int`, *optional*):
The current timestep in the diffusion chain.
Returns:
`torch.FloatTensor`:
A scaled input sample.
"""
# Make sure sigmas and timesteps have the same device and dtype as original_samples
sigmas = self.sigmas.to(device=sample.device, dtype=sample.dtype)
if sample.device.type == "mps" and torch.is_floating_point(timestep):
# mps does not support float64
schedule_timesteps = self.timesteps.to(sample.device, dtype=self.dtype)
timestep = timestep.to(sample.device, dtype=self.dtype)
else:
schedule_timesteps = self.timesteps.to(sample.device)
timestep = timestep.to(sample.device)
# self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index
if self.begin_index is None:
step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timestep]
elif self.step_index is not None:
# add_noise is called after first denoising step (for inpainting)
step_indices = [self.step_index] * timestep.shape[0]
else:
# add noise is called before first denoising step to create initial latent(img2img)
step_indices = [self.begin_index] * timestep.shape[0]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(sample.shape):
sigma = sigma.unsqueeze(-1)
sample = sigma * noise + (1.0 - sigma) * sample
return sample
def _sigma_to_t(self, sigma):
return sigma * self.config.num_train_timesteps
def index_for_timestep(self, timestep, schedule_timesteps):
"""
Get the index for a given timestep in the schedule.
Args:
timestep (`torch.Tensor`):
The timestep to find the index for.
schedule_timesteps (`torch.Tensor`):
The schedule timesteps.
Returns:
`int`:
The index for the timestep.
"""
# Find the closest timestep in the schedule
indices = torch.searchsorted(schedule_timesteps, timestep, right=True)
indices = torch.clamp(indices, 0, len(schedule_timesteps) - 1)
return indices.item()
def step(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = True,
**kwargs
) -> torch.Tensor:
'''
One step of the STORK update for flow matching or noise-based diffusion models.
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`, defaults to `True`):
Whether or not to return a [`~schedulers.STORKSchedulerOutput`] instead of a plain tuple.
Returns:
result (Union[Tuple, STORKSchedulerOutput]):
The next sample in the diffusion chain, either as a tuple or as a [`~schedulers.STORKSchedulerOutput`]. The value is converted back to the original dtype of `model_output` to avoid numerical issues.
'''
original_model_output_dtype = model_output.dtype
# Cast model_output and sample to "torch.float32" to avoid numerical issues
model_output = model_output.to(self.dtype)
sample = sample.to(self.dtype)
# Move sample to model_output's device
sample = sample.to(model_output.device)
"""
self.velocity_predictions always contain upcasted model_output in torch.float32 dtype.
"""
if self.prediction_type == "epsilon":
if self.solver_order == 2:
result = self.step_noise_2(model_output, timestep, sample, return_dict)
elif self.solver_order == 4:
result = self.step_noise_4(model_output, timestep, sample, return_dict)
else:
raise ValueError(f"Solver order {self.solver_order} is not yet supported for noise-based models")
elif self.prediction_type == "flow_prediction":
if self.solver_order == 1:
result = self.step_flow_matching_1(model_output, timestep, sample, return_dict)
elif self.solver_order == 2:
result = self.step_flow_matching_2(model_output, timestep, sample, return_dict)
elif self.solver_order == 4:
result = self.step_flow_matching_4(model_output, timestep, sample, return_dict)
else:
raise ValueError(f"Solver order {self.solver_order} is not yet supported for flow matching models")
else:
raise ValueError(f"Prediction type {self.prediction_type} is not yet supported")
# Convert the result back to the original dtype of model_output, as this result will be used as the next input to the model
if return_dict:
result.prev_sample = result.prev_sample.to(original_model_output_dtype)
else:
result = (result[0].to(original_model_output_dtype),)
return result
def step_flow_matching_1(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = False
) -> torch.Tensor:
# Initialize the step index if it's the first step
if self._step_index is None:
self._step_index = 0
# Compute the startup phase or the derivative approximation for the main step
if self._step_index == 0:
img_next = sample - model_output * self.dt_list[self._step_index]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
t = self.sigmas[self._step_index]
t_start = torch.ones(model_output.shape, device=sample.device) * t
t_next = self.sigmas[self._step_index + 1]
h1 = self.dt_list[self._step_index-1]
if self.derivative_order == 1:
# Ensure h1 is a tensor for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (self.velocity_predictions[-1] - model_output) / h1_tensor
velocity_second_derivative = None
velocity_third_derivative = None
elif self.derivative_order == 2:
# Ensure h1 and h2 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
if self._step_index == 1:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = self.dt_list[self._step_index-2]
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (-self.velocity_predictions[-2] + 4 * self.velocity_predictions[-1] - 3 * model_output) / (2 * h1_tensor)
velocity_second_derivative = 2 / (h1_tensor * h2_tensor * (h1_tensor + h2_tensor)) * (self.velocity_predictions[-2] * h1_tensor - self.velocity_predictions[-1] * (h1_tensor + h2_tensor) + model_output * h2_tensor)
velocity_third_derivative = None
elif self.derivative_order == 3:
if self._step_index == 1 or self._step_index == 2:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = h1 + self.dt_list[self._step_index-2]
h3 = h2 + self.dt_list[self._step_index-3]
# Ensure h1, h2, and h3 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
h3_tensor = torch.tensor(h3, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = ((h2_tensor * h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor * h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor * h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_second_derivative = 2 * ((h2_tensor + h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor + h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor + h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_third_derivative = 6 * ((h2_tensor - h3_tensor) * (self.velocity_predictions[-1] - model_output) + (h3_tensor - h1_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor - h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
else:
print("The noise approximation order is not supported!")
exit()
self.velocity_predictions.append(model_output)
self._step_index += 1
Y_j_2 = sample
Y_j_1 = sample
Y_j = sample
# Implementation of our Runge-Kutta-Gegenbauer second order method
for j in range(1, self.s + 1):
# Calculate the corresponding \bar{alpha}_t and beta_t that aligns with the correct timestep
fraction = (j - 1) * (j + 2) / (self.s * (self.s + 3))
if j == 1:
mu_tilde = 4 / (self.s * (self.s + 1))
dt = (t - t_next) * torch.ones(model_output.shape, device=sample.device)
Y_j = Y_j_1 - dt * mu_tilde * model_output
else:
mu = (2 * j + 1) * self.coeff_rock1(j) / (j * self.coeff_rock1(j - 1))
nu = -(j + 1) * self.coeff_rock1(j) / (j * self.coeff_rock1(j - 2))
mu_tilde = mu * 4 / (self.s * (self.s + 1))
# Probability flow ODE update
diff = -fraction * (t - t_next) * torch.ones(model_output.shape, device=sample.device)
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j = mu * Y_j_1 + nu * Y_j_2 - dt * mu_tilde * velocity
Y_j_2 = Y_j_1
Y_j_1 = Y_j
img_next = Y_j
img_next = img_next.to(model_output.dtype)
return SchedulerOutput(prev_sample=img_next)
def step_flow_matching_2(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = False,
) -> torch.Tensor:
'''
One step of the STORK2 update for flow matching based models.
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`, defaults to `True`):
Whether or not to return a [`~schedulers.STORKSchedulerOutput`] instead of a plain tuple.
Returns:
result (Union[Tuple, STORKSchedulerOutput]):
The next sample in the diffusion chain, either as a tuple or as a [`~schedulers.STORKSchedulerOutput`]. The value is converted back to the original dtype of `model_output` to avoid numerical issues.
'''
# Initialize the step index if it's the first step
if self._step_index is None:
self._step_index = 0
# Compute the startup phase or the derivative approximation for the main step
if self._step_index == 0:
img_next = sample - model_output * self.dt_list[self._step_index]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
t = self.sigmas[self._step_index]
t_start = torch.ones(model_output.shape, device=sample.device) * t
t_next = self.sigmas[self._step_index + 1]
h1 = self.dt_list[self._step_index-1]
if self.derivative_order == 1:
# Ensure h1 is a tensor for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (self.velocity_predictions[-1] - model_output) / h1_tensor
velocity_second_derivative = None
velocity_third_derivative = None
elif self.derivative_order == 2:
# Ensure h1 and h2 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
if self._step_index == 1:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = self.dt_list[self._step_index-2]
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (-self.velocity_predictions[-2] + 4 * self.velocity_predictions[-1] - 3 * model_output) / (2 * h1_tensor)
velocity_second_derivative = 2 / (h1_tensor * h2_tensor * (h1_tensor + h2_tensor)) * (self.velocity_predictions[-2] * h1_tensor - self.velocity_predictions[-1] * (h1_tensor + h2_tensor) + model_output * h2_tensor)
velocity_third_derivative = None
elif self.derivative_order == 3:
if self._step_index == 1 or self._step_index == 2:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = h1 + self.dt_list[self._step_index-2]
h3 = h2 + self.dt_list[self._step_index-3]
# Ensure h1, h2, and h3 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
h3_tensor = torch.tensor(h3, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = ((h2_tensor * h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor * h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor * h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_second_derivative = 2 * ((h2_tensor + h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor + h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor + h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_third_derivative = 6 * ((h2_tensor - h3_tensor) * (self.velocity_predictions[-1] - model_output) + (h3_tensor - h1_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor - h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
else:
print("The noise approximation order is not supported!")
exit()
self.velocity_predictions.append(model_output)
self._step_index += 1
Y_j_2 = sample
Y_j_1 = sample
Y_j = sample
# Implementation of our Runge-Kutta-Gegenbauer second order method
for j in range(1, self.s + 1):
# Calculate the corresponding \bar{alpha}_t and beta_t that aligns with the correct timestep
if j > 1:
if j == 2:
fraction = 4 / (3 * (self.s**2 + self.s - 2))
else:
fraction = ((j - 1)**2 + (j - 1) - 2) / (self.s**2 + self.s - 2)
if j == 1:
mu_tilde = 6 / ((self.s + 4) * (self.s - 1))
dt = (t - t_next) * torch.ones(model_output.shape, device=sample.device)
Y_j = Y_j_1 - dt * mu_tilde * model_output
else:
mu = (2 * j + 1) * self.b_coeff(j) / (j * self.b_coeff(j - 1))
nu = -(j + 1) * self.b_coeff(j) / (j * self.b_coeff(j - 2))
mu_tilde = mu * 6 / ((self.s + 4) * (self.s - 1))
gamma_tilde = -mu_tilde * (1 - j * (j + 1) * self.b_coeff(j-1)/ 2)
# Probability flow ODE update
diff = -fraction * (t - t_next) * torch.ones(model_output.shape, device=sample.device)
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j = mu * Y_j_1 + nu * Y_j_2 + (1 - mu - nu) * sample - dt * mu_tilde * velocity - dt * gamma_tilde * model_output
Y_j_2 = Y_j_1
Y_j_1 = Y_j
img_next = Y_j
img_next = img_next.to(model_output.dtype)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
def step_flow_matching_4(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = False,
) -> torch.Tensor:
'''
One step of the STORK4 update for flow matching models
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.FloatTensor`: The next sample in the diffusion chain.
'''
# Initialize the step index if it's the first step
if self._step_index is None:
self._step_index = 0
# Compute the startup phase or the derivative approximation for the main step
if self._step_index == 0:
img_next = sample - model_output * self.dt_list[self._step_index]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
t = self.sigmas[self._step_index]
t_start = torch.ones(model_output.shape, device=sample.device) * t
t_next = self.sigmas[self._step_index + 1]
h1 = self.dt_list[self._step_index-1]
if self.derivative_order == 1:
# Ensure h1 is a tensor for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (self.velocity_predictions[-1] - model_output) / h1_tensor
velocity_second_derivative = None
velocity_third_derivative = None
elif self.derivative_order == 2:
# Ensure h1 and h2 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
if self._step_index == 1:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = self.dt_list[self._step_index-2]
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = (-self.velocity_predictions[-2] + 4 * self.velocity_predictions[-1] - 3 * model_output) / (2 * h1_tensor)
velocity_second_derivative = 2 / (h1_tensor * h2_tensor * (h1_tensor + h2_tensor)) * (self.velocity_predictions[-2] * h1_tensor - self.velocity_predictions[-1] * (h1_tensor + h2_tensor) + model_output * h2_tensor)
velocity_third_derivative = None
elif self.derivative_order == 3:
if self._step_index == 1 or self._step_index == 2:
img_next = sample - 1.5 * model_output * self.dt_list[self._step_index] + 0.5 * self.velocity_predictions[-1] * self.dt_list[self._step_index-1]
self._step_index += 1
self.velocity_predictions.append(model_output)
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
else:
h2 = h1 + self.dt_list[self._step_index-2]
h3 = h2 + self.dt_list[self._step_index-3]
# Ensure h1, h2, and h3 are tensors for proper broadcasting
h1_tensor = torch.tensor(h1, device=model_output.device, dtype=model_output.dtype)
h2_tensor = torch.tensor(h2, device=model_output.device, dtype=model_output.dtype)
h3_tensor = torch.tensor(h3, device=model_output.device, dtype=model_output.dtype)
velocity_derivative = ((h2_tensor * h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor * h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor * h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_second_derivative = 2 * ((h2_tensor + h3_tensor) * (self.velocity_predictions[-1] - model_output) - (h1_tensor + h3_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor + h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
velocity_third_derivative = 6 * ((h2_tensor - h3_tensor) * (self.velocity_predictions[-1] - model_output) + (h3_tensor - h1_tensor) * (self.velocity_predictions[-2] - model_output) + (h1_tensor - h2_tensor) * (self.velocity_predictions[-3] - model_output)) / (h1_tensor * h2_tensor * h3_tensor)
else:
print("The noise approximation order is not supported!")
exit()
self.velocity_predictions.append(model_output)
self._step_index += 1
Y_j_2 = sample
Y_j_1 = sample
Y_j = sample
ci1 = t_start
ci2 = t_start
ci3 = t_start
# Coefficients of ROCK4
ms, fpa, fpb, fpbe, recf = self.coeff_rock4()
# Choose the degree that's in the precomputed table
mdeg, mp = self.mdegr(self.s, ms)
mz = int(mp[0])
mr = int(mp[1])
'''
The first part of the STORK4 update
'''
for j in range(1, mdeg + 1):
# First sub-step in the first part of the STORK4 update
if j == 1:
temp1 = -(t - t_next) * recf[mr] * torch.ones(model_output.shape, device=sample.device)
ci1 = t_start + temp1
ci2 = ci1
Y_j_1 = sample + temp1 * model_output
# Y_j = sample + temp1 * model_output
# Second and the following sub-steps in the first part of the STORK4 update
else:
diff = ci1 - t_start
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
temp1 = -(t - t_next) * recf[mr + 2 * (j-2) + 1] * torch.ones(model_output.shape, device=sample.device)
temp3 = -recf[mr + 2 * (j-2) + 2] * torch.ones(model_output.shape, device=sample.device)
temp2 = torch.ones(model_output.shape, device=sample.device) - temp3
ci1 = temp1 + temp2 * ci2 + temp3 * ci3
Y_j = temp1 * velocity + temp2 * Y_j_1 + temp3 * Y_j_2
# Update the intermediate variables
Y_j_2 = Y_j_1
Y_j_1 = Y_j
ci3 = ci2
ci2 = ci1
'''
The finishing four-step procedure as a composition method
'''
# First finishing step
temp1 = -(t - t_next) * fpa[mz,0] * torch.ones(model_output.shape, device=sample.device)
diff = ci1 - t_start
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j_1 = velocity
Y_j_3 = Y_j + temp1 * Y_j_1
# Second finishing step
ci2 = ci1 + temp1
temp1 = -(t - t_next) * fpa[mz,1] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpa[mz,2] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j_2 = velocity
Y_j_4 = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2
# Third finishing step
ci2 = ci1 + temp1 + temp2
temp1 = -(t - t_next) * fpa[mz,3] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpa[mz,4] * torch.ones(model_output.shape, device=sample.device)
temp3 = -(t - t_next) * fpa[mz,5] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j_3 = velocity
# This is the counterpart of the final step in the noise-based diffusion models STORK4
# fnt = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2 + temp3 * Y_j_3
# Fourth finishing step
ci2 = ci1 + temp1 + temp2 + temp3
temp1 = -(t - t_next) * fpb[mz,0] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpb[mz,1] * torch.ones(model_output.shape, device=sample.device)
temp3 = -(t - t_next) * fpb[mz,2] * torch.ones(model_output.shape, device=sample.device)
temp4 = -(t - t_next) * fpb[mz,3] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, velocity_derivative, velocity_second_derivative, velocity_third_derivative)
Y_j_4 = velocity
Y_j = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2 + temp3 * Y_j_3 + temp4 * Y_j_4
img_next = Y_j
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
def step_noise_2(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = False,
) -> torch.Tensor:
'''
One step of the STORK2 update for noise-based diffusion models.
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`, defaults to `True`):
Whether or not to return a [`~schedulers.STORKSchedulerOutput`] instead of a plain tuple.
Returns:
`torch.FloatTensor`: The next sample in the diffusion chain.
'''
# Initialize the step index if it's the first step
if self._step_index is None:
self._step_index = 0
self.initial_noise = model_output
total_step = self.config.num_train_timesteps
t = self.timesteps[self._step_index] / total_step
beta_0, beta_1 = self.betas[0], self.betas[-1]
t_start = torch.ones(model_output.shape, device=sample.device) * t
beta_t = (beta_0 + t_start * (beta_1 - beta_0)) * total_step
log_mean_coeff = (-0.25 * t_start ** 2 * (beta_1 - beta_0) - 0.5 * t_start * beta_0) * total_step
std = torch.sqrt(1. - torch.exp(2. * log_mean_coeff))
# Tweedie's trick
if self._step_index == len(self.timesteps) - 1:
noise_last = model_output
img_next = sample - std * noise_last
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
t_next = self.timesteps[self._step_index + 1] / total_step
# drift, diffusion -> f(x,t), g(t)
drift_initial, diffusion_initial = -0.5 * beta_t * sample, torch.sqrt(beta_t) * torch.ones(sample.shape, device=sample.device)
noise_initial = model_output
score = -noise_initial / std # score -> noise
drift_initial = drift_initial - diffusion_initial ** 2 * score * 0.5 # drift -> dx/dt
dt = torch.ones(model_output.shape, device=sample.device) * self.dt
if self._step_index == 0:
# FIRST RUN
self.initial_sample = sample
img_next = sample - 0.5 * dt * drift_initial
self.noise_predictions.append(noise_initial)
self._step_index += 1
self.initial_sample = sample
self.initial_drift = drift_initial
self.initial_noise = model_output
return SchedulerOutput(prev_sample=img_next)
elif self._step_index == 1:
# SECOND RUN
t_previous = torch.ones(model_output.shape, device=sample.device) * self.timesteps[0] / 1000
drift_previous = self.drift_function(self.betas, self.config.num_train_timesteps, t_previous, self.initial_sample, self.noise_predictions[-1])
img_next = sample - 0.75 * dt * drift_initial + 0.25 * dt * drift_previous
self.noise_predictions.append(noise_initial)
self._step_index += 1
return SchedulerOutput(prev_sample=img_next)
elif self._step_index == 2:
h = 0.5 * dt
noise_derivative = (3 * self.noise_predictions[0] - 4 * self.noise_predictions[1] + model_output) / (2 * h)
noise_second_derivative = (self.noise_predictions[0] - 2 * self.noise_predictions[1] + model_output) / (h ** 2)
noise_third_derivative = None
model_output = self.initial_noise
drift_initial = self.initial_drift
sample = self.initial_sample
t = self.timesteps[0] / total_step
t_start = torch.ones(model_output.shape, device=sample.device) * t
t_next = self.timesteps[2] / total_step
elif self._step_index == 3:
h = 0.5 * dt
noise_derivative = (-3 * noise_initial + 4 * self.noise_predictions[-1] - self.noise_predictions[-2]) / (2 * h)
noise_second_derivative = (noise_initial - 2 * self.noise_predictions[-1] + self.noise_predictions[-2]) / (h ** 2)
noise_third_derivative = None
self.noise_predictions.append(noise_initial)
elif self._step_index == 4:
h = dt
noise_derivative = (-3 * noise_initial + 4 * self.noise_predictions[-1] - self.noise_predictions[-2]) / (2 * h)
noise_second_derivative = (noise_initial - 2 * self.noise_predictions[-1] + self.noise_predictions[-2]) / (h ** 2)
noise_third_derivative = None
self.noise_predictions.append(noise_initial)
else:
# ALL ELSE
h = dt
noise_derivative = (2 * self.noise_predictions[-3] - 9 * self.noise_predictions[-2] + 18 * self.noise_predictions[-1] - 11 * noise_initial) / (6 * h)
noise_second_derivative = (-self.noise_predictions[-3] + 4 * self.noise_predictions[-2] -5 * self.noise_predictions[-1] + 2 * noise_initial) / (h**2)
noise_third_derivative = (self.noise_predictions[-3] - 3 * self.noise_predictions[-2] + 3 * self.noise_predictions[-1] - noise_initial) / (h**3)
self.noise_predictions.append(noise_initial)
Y_j_2 = sample
Y_j_1 = sample
Y_j = sample
# Implementation of our Runge-Kutta-Gegenbauer second order method
for j in range(1, self.s + 1):
# Calculate the corresponding \bar{alpha}_t and beta_t that aligns with the correct timestep
if j > 1:
if j == 2:
fraction = 4 / (3 * (self.s**2 + self.s - 2))
else:
fraction = ((j - 1)**2 + (j - 1) - 2) / (self.s**2 + self.s - 2)
if j == 1:
mu_tilde = 6 / ((self.s + 4) * (self.s - 1))
dt = (t - t_next) * torch.ones(model_output.shape, device=sample.device)
Y_j = Y_j_1 - dt * mu_tilde * model_output
else:
mu = (2 * j + 1) * self.b_coeff(j) / (j * self.b_coeff(j - 1))
nu = -(j + 1) * self.b_coeff(j) / (j * self.b_coeff(j - 2))
mu_tilde = mu * 6 / ((self.s + 4) * (self.s - 1))
gamma_tilde = -mu_tilde * (1 - j * (j + 1) * self.b_coeff(j-1)/ 2)
# Probability flow ODE update
diff = -fraction * (t - t_next) * torch.ones(model_output.shape, device=sample.device)
velocity = self.taylor_approximation(self.derivative_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
Y_j = mu * Y_j_1 + nu * Y_j_2 + (1 - mu - nu) * sample - dt * mu_tilde * velocity - dt * gamma_tilde * model_output
Y_j_2 = Y_j_1
Y_j_1 = Y_j
img_next = Y_j
img_next = img_next.to(model_output.dtype)
self._step_index += 1
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
def step_noise_4(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor = None,
return_dict: bool = False,
) -> torch.Tensor:
'''
One step of the STORK4 update for noise-based diffusion models.
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`, defaults to `True`):
Whether or not to return a [`~schedulers.STORKSchedulerOutput`] instead of a plain tuple.
Returns:
`torch.FloatTensor`: The next sample in the diffusion chain.
'''
# Initialize the step index if it's the first step
if self._step_index is None:
self._step_index = 0
self.initial_noise = model_output
total_step = self.config.num_train_timesteps
t = self.timesteps[self._step_index] / total_step
beta_0, beta_1 = self.betas[0], self.betas[-1]
t_start = torch.ones(model_output.shape, device=sample.device) * t
beta_t = (beta_0 + t_start * (beta_1 - beta_0)) * total_step
log_mean_coeff = (-0.25 * t_start ** 2 * (beta_1 - beta_0) - 0.5 * t_start * beta_0) * total_step
std = torch.sqrt(1. - torch.exp(2. * log_mean_coeff))
# Tweedie's trick
if self._step_index == len(self.timesteps) - 1:
noise_last = model_output
img_next = sample - std * noise_last
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
t_next = self.timesteps[self._step_index + 1] / total_step
# drift, diffusion -> f(x,t), g(t)
drift_initial, diffusion_initial = -0.5 * beta_t * sample, torch.sqrt(beta_t) * torch.ones(sample.shape, device=sample.device)
noise_initial = model_output
score = -noise_initial / std # score -> noise
drift_initial = drift_initial - diffusion_initial ** 2 * score * 0.5 # drift -> dx/dt
dt = torch.ones(model_output.shape, device=sample.device) * self.dt
if self.derivative_order == 2:
if self._step_index == 0:
# Initial Euler update
self.initial_sample = sample
img_next = sample - dt * drift_initial
self.noise_predictions.append(noise_initial)
self._step_index += 1
self.initial_drift = drift_initial
if not return_dict:
return (img_next,)
return SchedulerOutput(prev_sample=img_next)
elif self._step_index == 1:
# Initial 2-step Adams-Bashforth update
drift_previous = self.initial_drift
img_next = sample - 1.5 * dt * drift_initial + 0.5 * dt * drift_previous
self.noise_predictions.append(noise_initial)
self._step_index += 1
if not return_dict:
return (img_next,)
return SchedulerOutput(prev_sample=img_next)
else:
# STORK4 update
h = dt
# The first derivative is calculated using the three point approximation,
# and the second derivative is calculated using the standardtwo point approximation.
noise_derivative = (-self.noise_predictions[-2] + 4 * self.noise_predictions[-1] - 3 * noise_initial) / (2 * h)
noise_second_derivative = (self.noise_predictions[-2] - 2 * self.noise_predictions[-1] + noise_initial) / h**2
noise_third_derivative = None
self.noise_predictions.append(noise_initial)
noise_approx_order = 2
elif self.derivative_order == 1:
if self._step_index == 0:
# Initial Euler update
self.initial_sample = sample
img_next = sample - dt * drift_initial
self.noise_predictions.append(noise_initial)
self._step_index += 1
self.initial_drift = drift_initial
if not return_dict:
return (img_next,)
return SchedulerOutput(prev_sample=img_next)
else:
# STORK4 update
h = dt
noise_derivative = (self.noise_predictions[-1] - noise_initial) / h
noise_second_derivative = None
noise_third_derivative = None
self.noise_predictions.append(noise_initial)
noise_approx_order = 1
else:
raise ValueError(f"Unknown derivative order: {self.derivative_order}")
Y_j_2 = sample
Y_j_1 = sample
Y_j = sample
ci1 = t_start
ci2 = t_start
ci3 = t_start
# Coefficients of ROCK4
ms, fpa, fpb, fpbe, recf = self.coeff_rock4()
# Choose the degree that's in the precomputed table
mdeg, mp = self.mdegr(self.s, ms)
mz = int(mp[0])
mr = int(mp[1])
'''
The first part of the STORK4 update
'''
for j in range(1, mdeg + 1):
# First sub-step in the first part of the STORK4 update
if j == 1:
temp1 = -(t - t_next) * recf[mr] * torch.ones(model_output.shape, device=sample.device)
ci1 = t_start + temp1
ci2 = ci1
Y_j_1 = sample + temp1 * model_output #subver
# drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, t_start, Y_j, model_output)
# Y_j_1 = sample + temp1 * drift_approx
# Second and the following sub-steps in the first part of the STORK4 update
else:
diff = ci1 - t_start
noise_approx = self.taylor_approximation(noise_approx_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, ci1, Y_j_1, noise_approx)
temp1 = -(t - t_next) * recf[mr + 2 * (j-2) + 1] * torch.ones(model_output.shape, device=sample.device)
temp3 = -recf[mr + 2 * (j-2) + 2] * torch.ones(model_output.shape, device=sample.device)
temp2 = torch.ones(model_output.shape, device=sample.device) - temp3
ci1 = temp1 + temp2 * ci2 + temp3 * ci3
Y_j = temp1 * drift_approx + temp2 * Y_j_1 + temp3 * Y_j_2
# Update the intermediate variables
Y_j_2 = Y_j_1
Y_j_1 = Y_j
ci3 = ci2
ci2 = ci1
'''
The finishing four-step procedure as a composition method
'''
# First finishing step
temp1 = -(t - t_next) * fpa[mz,0] * torch.ones(model_output.shape, device=sample.device)
diff = ci1 - t_start
noise_approx = self.taylor_approximation(noise_approx_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, ci1, Y_j, noise_approx)
Y_j_1 = drift_approx
Y_j_3 = Y_j + temp1 * Y_j_1
# Second finishing step
ci2 = ci1 + temp1
temp1 = -(t - t_next) * fpa[mz,1] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpa[mz,2] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
noise_approx = self.taylor_approximation(noise_approx_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, ci2, Y_j_3, noise_approx)
Y_j_2 = drift_approx
Y_j_4 = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2
# Third finishing step
ci2 = ci1 + temp1 + temp2
temp1 = -(t - t_next) * fpa[mz,3] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpa[mz,4] * torch.ones(model_output.shape, device=sample.device)
temp3 = -(t - t_next) * fpa[mz,5] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
noise_approx = self.taylor_approximation(noise_approx_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, ci2, Y_j_4, noise_approx)
Y_j_3 = drift_approx
fnt = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2 + temp3 * Y_j_3
# Fourth finishing step
ci2 = ci1 + temp1 + temp2 + temp3
temp1 = -(t - t_next) * fpb[mz,0] * torch.ones(model_output.shape, device=sample.device)
temp2 = -(t - t_next) * fpb[mz,1] * torch.ones(model_output.shape, device=sample.device)
temp3 = -(t - t_next) * fpb[mz,2] * torch.ones(model_output.shape, device=sample.device)
temp4 = -(t - t_next) * fpb[mz,3] * torch.ones(model_output.shape, device=sample.device)
diff = ci2 - t_start
noise_approx = self.taylor_approximation(noise_approx_order, diff, model_output, noise_derivative, noise_second_derivative, noise_third_derivative)
drift_approx = self.drift_function(self.betas, self.config.num_train_timesteps, ci2, fnt, noise_approx)
Y_j_4 = drift_approx
Y_j = Y_j + temp1 * Y_j_1 + temp2 * Y_j_2 + temp3 * Y_j_3 + temp4 * Y_j_4
img_next = Y_j
self._step_index += 1
if not return_dict:
return (img_next,)
return STORKSchedulerOutput(prev_sample=img_next)
def __len__(self):
return self.config.num_train_timesteps
def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor:
"""
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Args:
sample (`torch.Tensor`):
The input sample.
Returns:
`torch.Tensor`:
A scaled input sample.
"""
return sample
def add_noise(
self,
original_samples: torch.FloatTensor,
noise: torch.FloatTensor,
timesteps: torch.IntTensor,
) -> torch.FloatTensor:
"""
Add noise to the original samples according to the noise magnitude at the given timestep.
Args:
original_samples (`torch.FloatTensor`):
The original samples.
noise (`torch.FloatTensor`):
The noise to add.
timesteps (`torch.IntTensor`):
The timesteps for which to add noise.
Returns:
`torch.FloatTensor`:
The noisy samples.
"""
# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
timesteps = timesteps.to(original_samples.device)
sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
return noisy_samples
def get_velocity(
self,
sample: torch.FloatTensor,
noise: torch.FloatTensor,
timesteps: torch.IntTensor,
) -> torch.FloatTensor:
"""
Get the velocity (score) for the given sample, noise, and timesteps.
Args:
sample (`torch.FloatTensor`):
The sample.
noise (`torch.FloatTensor`):
The noise.
timesteps (`torch.IntTensor`):
The timesteps.
Returns:
`torch.FloatTensor`:
The velocity.
"""
# Make sure alphas_cumprod and timestep have same device and dtype as sample
alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
timesteps = timesteps.to(sample.device)
sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
while len(sqrt_alpha_prod.shape) < len(sample.shape):
sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
return velocity
def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
if self.config.time_shift_type == "exponential":
return self._time_shift_exponential(mu, sigma, t)
elif self.config.time_shift_type == "linear":
return self._time_shift_linear(mu, sigma, t)
def _time_shift_exponential(self, mu, sigma, t):
return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)
def _time_shift_linear(self, mu, sigma, t):
return mu / (mu + (1 / t - 1) ** sigma)
def taylor_approximation(self, taylor_approx_order, diff, model_output, derivative, second_derivative, third_derivative=None):
if taylor_approx_order == 1:
approx_value = model_output + diff * derivative
elif taylor_approx_order == 2:
if third_derivative is not None:
raise ValueError("The third derivative is computed but not used!")
approx_value = model_output + diff * derivative + 0.5 * diff**2 * second_derivative
elif taylor_approx_order == 3:
if third_derivative is None:
raise ValueError("The third derivative is not computed!")
approx_value = model_output + diff * derivative + 0.5 * diff**2 * second_derivative \
+ diff**3 * third_derivative / 6
else:
print("The noise approximation order is not supported!")
exit()
return approx_value
def drift_function(self, betas, total_step, t_eval, y_eval, noise):
'''
Drift function for the probability flow ODE in the noise-based diffusion model.
Args:
betas (`torch.FloatTensor`):
The betas of the diffusion model.
total_step (`int`):
The total number of steps in the diffusion chain.
t_eval (`torch.FloatTensor`):
The timestep to be evaluated at in the diffusion chain.
y_eval (`torch.FloatTensor`):
The sample to be evaluated at in the diffusion chain.
noise (`torch.FloatTensor`):
The noise used at the current timestep in the diffusion chain.
Returns:
`torch.FloatTensor`:
The drift term for the probability flow ODE in the diffusion model.
'''
beta_0, beta_1 = betas[0], betas[-1]
beta_t = (beta_0 + t_eval * (beta_1 - beta_0)) * total_step
beta_t = beta_t * torch.ones(y_eval.shape, device=y_eval.device)
log_mean_coeff = (-0.25 * t_eval ** 2 * (beta_1 - beta_0) - 0.5 * t_eval * beta_0) * total_step
std = torch.sqrt(1. - torch.exp(2. * log_mean_coeff))
# drift, diffusion -> f(x,t), g(t)
drift, diffusion = -0.5 * beta_t * y_eval, torch.sqrt(beta_t) * torch.ones(y_eval.shape, device=y_eval.device)
score = -noise / std # score -> noise
drift = drift - diffusion ** 2 * score * 0.5 # drift -> dx/dt
return drift
def b_coeff(self, j):
'''
Coefficients of STORK2. The are based on the second order Runge-Kutta-Gegenbauer method.
Details of the coefficients can be found in https://www.sciencedirect.com/science/article/pii/S0021999120306537
Args:
j (`int`):
The sub-step index of the coefficient.
Returns:
`float`:
The coefficient of the STORK2.
'''
if j < 0:
print("The b_j coefficient in the RKG method can't have j negative")
return
if j == 0:
return 1
if j == 1:
return 1 / 3
return 4 * (j - 1) * (j + 4) / (3 * j * (j + 1) * (j + 2) * (j + 3))
def coeff_rock1(self, j):
if j < 0:
print("The b_j coefficient in the RKG method can't have j negative")
return 2 / ((j + 1) * (j + 2))
def coeff_rock4(self):
'''
Load pre-computed coefficients of STORK4. The are based on the fourth order orthogonal Runge-Kutta-Chebyshev (ROCK4) method.
Details of the coefficients can be found in https://epubs.siam.org/doi/abs/10.1137/S1064827500379549.
The pre-computed coefficients are based on the implementation https://www.mathworks.com/matlabcentral/fileexchange/12129-rock4.
Args:
j (`int`):
The sub-step index of the coefficient.
Returns:
ms (`torch.FloatTensor`):
The degrees that coefficients were pre-computed for STORK4.
fpa, fpb, fpbe, recf (`torch.FloatTensor`):
The parameters for the finishing procedure.
'''
# Degrees
data = loadmat(f'{CONSTANTSFOLDER}/ms.mat')
ms = data['ms'][0]
# Parameters for the finishing procedure
data = loadmat(f'{CONSTANTSFOLDER}/fpa.mat')
fpa = data['fpa']
data = loadmat(f'{CONSTANTSFOLDER}/fpb.mat')
fpb = data['fpb']
data = loadmat(f'{CONSTANTSFOLDER}/fpbe.mat')
fpbe = data['fpbe']
# Parameters for the recurrence procedure
data = loadmat(f'{CONSTANTSFOLDER}/recf.mat')
recf = data['recf'][0]
return ms, fpa, fpb, fpbe, recf
def mdegr(self, mdeg1, ms):
'''
Find the optimal degree in the pre-computed degree coefficients table for the STORK4 method.
Args:
mdeg1 (`int`):
The degree to be evaluated.
ms (`torch.FloatTensor`):
The degrees that coefficients were pre-computed for STORK4.
Returns:
mdeg (`int`):
The optimal degree in the pre-computed degree coefficients table for the STORK4 method.
mp (`torch.FloatTensor`):
The pointer which select the degree in ms[i], such that mdeg<=ms[i].
mp[0] (`int`): The pointer which select the degree in ms[i], such that mdeg<=ms[i].
mp[1] (`int`): The pointer which gives the corresponding position of a_1 in the data recf for the selected degree.
'''
mp = torch.zeros(2)
mp[1] = 1
mdeg = mdeg1
for i in range(len(ms)):
if (ms[i]/mdeg) >= 1:
mdeg = ms[i]
mp[0] = i
mp[1] = mp[1] - 1
break
else:
mp[1] = mp[1] + ms[i] * 2 - 1
return mdeg, mp |