scheduling_unipc_multistep
fastvideo.models.schedulers.scheduling_unipc_multistep.BaseScheduler
BaseScheduler(*args, **kwargs)fastvideo.models.schedulers.scheduling_unipc_multistep.BaseScheduler.set_shift
set_shift(shift: float) -> Nonefastvideo.models.schedulers.scheduling_unipc_multistep.BaseScheduler.set_timesteps
set_timesteps(*args, **kwargs) -> Nonefastvideo.models.schedulers.scheduling_unipc_multistep.BaseScheduler.scale_model_input
scale_model_input(sample: torch.Tensor, timestep: int | None = None) -> torch.Tensorfastvideo.models.schedulers.scheduling_unipc_multistep.betas_for_alpha_bar
betas_for_alpha_bar(num_diffusion_timesteps, max_beta = 0.999, alpha_transform_type = 'cosine')Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of (1-beta) over time from t = [0,1].
Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up to that part of the diffusion process.
Parameters
num_diffusion_timesteps: `int`the number of betas to produce.
max_beta: `float`the maximum beta to use; use values lower than 1 to prevent singularities.
alpha_transform_type: `str`, *optional*, default to `cosine`the type of noise schedule for alpha_bar. Choose from
cosineorexp
Returns
betas: `np.ndarray`the betas used by the scheduler to step the model outputs
Source
def betas_for_alpha_bar(
num_diffusion_timesteps,
max_beta=0.999,
alpha_transform_type="cosine",
):
"""
Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
(1-beta) over time from t = [0,1].
Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
to that part of the diffusion process.
Args:
num_diffusion_timesteps (`int`): the number of betas to produce.
max_beta (`float`): the maximum beta to use; use values lower than 1 to
prevent singularities.
alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
Choose from `cosine` or `exp`
Returns:
betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
"""
if alpha_transform_type == "cosine":
def alpha_bar_fn(t):
return math.cos((t + 0.008) / 1.008 * math.pi / 2)**2
elif alpha_transform_type == "exp":
def alpha_bar_fn(t):
return math.exp(t * -12.0)
else:
raise ValueError(f"Unsupported alpha_transform_type: {alpha_transform_type}")
betas = []
for i in range(num_diffusion_timesteps):
t1 = i / num_diffusion_timesteps
t2 = (i + 1) / num_diffusion_timesteps
betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
return torch.tensor(betas, dtype=torch.float32)</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.rescale_zero_terminal_snr
rescale_zero_terminal_snr(betas)
Rescales betas to have zero terminal SNR Based on https://huggingface.co/papers/2305.08891 (Algorithm 1)
Parameters
betas: `torch.Tensor`the betas that the scheduler is being initialized with.
Returns
torch.Tensor: rescaled betas with zero terminal SNR
Source
def rescale_zero_terminal_snr(betas):
"""
Rescales betas to have zero terminal SNR Based on https://huggingface.co/papers/2305.08891 (Algorithm 1)
Args:
betas (`torch.Tensor`):
the betas that the scheduler is being initialized with.
Returns:
`torch.Tensor`: rescaled betas with zero terminal SNR
"""
# Convert betas to alphas_bar_sqrt
alphas = 1.0 - betas
alphas_cumprod = torch.cumprod(alphas, dim=0)
alphas_bar_sqrt = alphas_cumprod.sqrt()
# Store old values.
alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
# Shift so the last timestep is zero.
alphas_bar_sqrt -= alphas_bar_sqrt_T
# Scale so the first timestep is back to the old value.
alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
# Convert alphas_bar_sqrt to betas
alphas_bar = alphas_bar_sqrt**2 # Revert sqrt
alphas = alphas_bar[1:] / alphas_bar[:-1] # Revert cumprod
alphas = torch.cat([alphas_bar[0:1], alphas])
betas = 1 - alphas
return betas</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler
UniPCMultistepScheduler(num_train_timesteps: int = 1000, beta_start: float = 0.0001, beta_end: float = 0.02, beta_schedule: str = 'linear', trained_betas: Optional[Union[np.ndarray, List[float]]] = None, solver_order: int = 2, prediction_type: str = 'epsilon', thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, predict_x0: bool = True, solver_type: str = 'bh2', lower_order_final: bool = True, disable_corrector: List[int] = [], solver_p: SchedulerMixin = None, use_karras_sigmas: Optional[bool] = False, use_exponential_sigmas: Optional[bool] = False, use_beta_sigmas: Optional[bool] = False, use_flow_sigmas: Optional[bool] = False, flow_shift: Optional[float] = 1.0, timestep_spacing: str = 'linspace', steps_offset: int = 0, final_sigmas_type: Optional[str] = 'zero', rescale_betas_zero_snr: bool = False, use_dynamic_shifting: bool = False, time_shift_type: str = 'exponential')
UniPCMultistepScheduler is a training-free framework designed for the fast sampling of diffusion models.
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.
Parameters
num_train_timesteps: `int`, defaults to 1000The number of diffusion steps to train the model.
beta_start: `float`, defaults to 0.0001The starting beta value of inference.
beta_end: `float`, defaults to 0.02The final beta value.
beta_schedule: `str`, defaults to `"linear"`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: `np.ndarray`, *optional*Pass an array of betas directly to the constructor to bypass beta_start and beta_end.
solver_order: `int`, default `2`The UniPC order which can be any positive integer. The effective order of accuracy is solver_order + 1
due to the UniC. It is recommended to use solver_order=2 for guided sampling, and solver_order=3 for
unconditional sampling.
prediction_type: `str`, defaults to `epsilon`, *optional*Prediction type of the scheduler function; can be epsilon (predicts the noise of the diffusion process),
sample (directly predicts the noisy sample) orv_prediction` (see section 2.4 of Imagen
Video paper).
thresholding: `bool`, defaults to `False`Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
as Stable Diffusion.
dynamic_thresholding_ratio: `float`, defaults to 0.995The ratio for the dynamic thresholding method. Valid only when thresholding=True.
sample_max_value: `float`, defaults to 1.0The threshold value for dynamic thresholding. Valid only when thresholding=True and predict_x0=True.
predict_x0: `bool`, defaults to `True`Whether to use the updating algorithm on the predicted x0.
solver_type: `str`, default `bh2`Solver type for UniPC. It is recommended to use bh1 for unconditional sampling when steps < 10, and bh2
otherwise.
lower_order_final: `bool`, default `True`Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
disable_corrector: `list`, default `[]`Decides which step to disable the corrector to mitigate the misalignment between epsilon_theta(x_t, c)
and epsilon_theta(x_t^c, c) which can influence convergence for a large guidance scale. Corrector is
usually disabled during the first few steps.
solver_p: `SchedulerMixin`, default `None`Any other scheduler that if specified, the algorithm becomes solver_p + UniC.
use_karras_sigmas: `bool`, *optional*, defaults to `False`Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If True,
the sigmas are determined according to a sequence of noise levels {σi}.
use_exponential_sigmas: `bool`, *optional*, defaults to `False`Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
use_beta_sigmas: `bool`, *optional*, defaults to `False`Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to Beta
Sampling is All You Need for more information.
use_flow_sigmas: `bool`, *optional*, defaults to `False`Whether to use flow sigmas for step sizes in the noise schedule during the sampling process.
timestep_spacing: `str`, defaults to `"linspace"`The way the timesteps should be scaled. Refer to Table 2 of the Common Diffusion Noise Schedules and
Sample Steps are Flawed for more information.
steps_offset: `int`, defaults to 0An offset added to the inference steps, as required by some model families.
final_sigmas_type: `str`, defaults to `"zero"`The final sigma value for the noise schedule during the sampling process. If "sigma_min", the final
sigma is the same as the last sigma in the training schedule. If zero, the final sigma is set to 0.
rescale_betas_zero_snr: `bool`, defaults to `False`Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
dark samples instead of limiting it to samples with medium brightness. Loosely related to
--offset_noise.
Source
class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin, BaseScheduler):
"""
`UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.
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.
beta_start (`float`, defaults to 0.0001):
The starting `beta` value of inference.
beta_end (`float`, defaults to 0.02):
The final `beta` value.
beta_schedule (`str`, defaults to `"linear"`):
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 (`np.ndarray`, *optional*):
Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
solver_order (`int`, default `2`):
The UniPC order which can be any positive integer. The effective order of accuracy is `solver_order + 1`
due to the UniC. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for
unconditional sampling.
prediction_type (`str`, defaults to `epsilon`, *optional*):
Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
`sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
Video](https://imagen.research.google/video/paper.pdf) paper).
thresholding (`bool`, defaults to `False`):
Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
as Stable Diffusion.
dynamic_thresholding_ratio (`float`, defaults to 0.995):
The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
sample_max_value (`float`, defaults to 1.0):
The threshold value for dynamic thresholding. Valid only when `thresholding=True` and `predict_x0=True`.
predict_x0 (`bool`, defaults to `True`):
Whether to use the updating algorithm on the predicted x0.
solver_type (`str`, default `bh2`):
Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
otherwise.
lower_order_final (`bool`, default `True`):
Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
disable_corrector (`list`, default `[]`):
Decides which step to disable the corrector to mitigate the misalignment between `epsilon_theta(x_t, c)`
and `epsilon_theta(x_t^c, c)` which can influence convergence for a large guidance scale. Corrector is
usually disabled during the first few steps.
solver_p (`SchedulerMixin`, default `None`):
Any other scheduler that if specified, the algorithm becomes `solver_p + UniC`.
use_karras_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
the sigmas are determined according to a sequence of noise levels {σi}.
use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
use_beta_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
use_flow_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use flow sigmas for step sizes in the noise schedule during the sampling process.
timestep_spacing (`str`, defaults to `"linspace"`):
The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
steps_offset (`int`, defaults to 0):
An offset added to the inference steps, as required by some model families.
final_sigmas_type (`str`, defaults to `"zero"`):
The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
rescale_betas_zero_snr (`bool`, defaults to `False`):
Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
dark samples instead of limiting it to samples with medium brightness. Loosely related to
[`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
order = 1
@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[Union[np.ndarray, List[float]]] = None,
solver_order: int = 2,
prediction_type: str = "epsilon",
thresholding: bool = False,
dynamic_thresholding_ratio: float = 0.995,
sample_max_value: float = 1.0,
predict_x0: bool = True,
solver_type: str = "bh2",
lower_order_final: bool = True,
disable_corrector: List[int] = [],
solver_p: SchedulerMixin = None,
use_karras_sigmas: Optional[bool] = False,
use_exponential_sigmas: Optional[bool] = False,
use_beta_sigmas: Optional[bool] = False,
use_flow_sigmas: Optional[bool] = False,
flow_shift: Optional[float] = 1.0,
timestep_spacing: str = "linspace",
steps_offset: int = 0,
final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min"
rescale_betas_zero_snr: bool = False,
use_dynamic_shifting: bool = False,
time_shift_type: str = "exponential",
):
if self.config.use_beta_sigmas and not is_scipy_available():
raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
if 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 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
elif beta_schedule == "squaredcos_cap_v2":
# Glide cosine schedule
self.betas = betas_for_alpha_bar(num_train_timesteps)
else:
raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
if rescale_betas_zero_snr:
self.betas = rescale_zero_terminal_snr(self.betas)
self.alphas = 1.0 - self.betas
self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
if rescale_betas_zero_snr:
# Close to 0 without being 0 so first sigma is not inf
# FP16 smallest positive subnormal works well here
self.alphas_cumprod[-1] = 2**-24
# Currently we only support VP-type noise schedule
self.alpha_t = torch.sqrt(self.alphas_cumprod)
self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod)**0.5
# standard deviation of the initial noise distribution
self.init_noise_sigma = 1.0
if solver_type not in ["bh1", "bh2"]:
if solver_type in ["midpoint", "heun", "logrho"]:
self.register_to_config(solver_type="bh2")
else:
raise NotImplementedError(f"{solver_type} is not implemented for {self.__class__}")
self.predict_x0 = predict_x0
# setable values
self.num_inference_steps = None
timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps)
self.num_train_timesteps = num_train_timesteps
self.model_outputs = [None] * solver_order
self.timestep_list = [None] * solver_order
self.lower_order_nums = 0
self.disable_corrector = disable_corrector
self.solver_p = solver_p
self.last_sample = None
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
BaseScheduler.__init__(self)
@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) -> None:
self.config.flow_shift = shift
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
def set_begin_index(self, begin_index: int = 0):
"""
Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
Args:
begin_index (`int`):
The begin index for the scheduler.
"""
self._begin_index = begin_index
def set_timesteps(self,
num_inference_steps: int,
device: Union[str, torch.device] = None,
mu: Optional[float] = None):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
num_inference_steps (`int`):
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.
"""
# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://huggingface.co/papers/2305.08891
if mu is not None:
assert self.config.use_dynamic_shifting and self.config.time_shift_type == "exponential"
self.config.flow_shift = np.exp(mu)
if self.config.timestep_spacing == "linspace":
timesteps = (np.linspace(0, self.config.num_train_timesteps - 1,
num_inference_steps + 1).round()[::-1][:-1].copy().astype(np.int64))
elif self.config.timestep_spacing == "leading":
step_ratio = self.config.num_train_timesteps // (num_inference_steps + 1)
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64)
timesteps += self.config.steps_offset
elif self.config.timestep_spacing == "trailing":
step_ratio = self.config.num_train_timesteps / num_inference_steps
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = np.arange(self.config.num_train_timesteps, 0, -step_ratio).round().copy().astype(np.int64)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
)
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod)**0.5)
if self.config.use_karras_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_exponential_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_beta_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_flow_sigmas:
alphas = np.linspace(1, 1 / self.config.num_train_timesteps, num_inference_steps + 1)
sigmas = 1.0 - alphas
sigmas = np.flip(self.config.flow_shift * sigmas / (1 + (self.config.flow_shift - 1) * sigmas))[:-1].copy()
timesteps = (sigmas * self.config.num_train_timesteps).copy()
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
else:
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
if self.config.final_sigmas_type == "sigma_min":
sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0])**0.5
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
self.sigmas = torch.from_numpy(sigmas)
self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
self.num_inference_steps = len(timesteps)
self.model_outputs = [
None,
] * self.config.solver_order
self.lower_order_nums = 0
self.last_sample = None
if self.solver_p:
self.solver_p.set_timesteps(self.num_inference_steps, device=device)
# add an index counter for schedulers that allow duplicated timesteps
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
"""
"Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
pixels from saturation at each step. We find that dynamic thresholding results in significantly better
photorealism as well as better image-text alignment, especially when using very large guidance weights."
https://huggingface.co/papers/2205.11487
"""
dtype = sample.dtype
batch_size, channels, *remaining_dims = sample.shape
if dtype not in (torch.float32, torch.float64):
sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half
# Flatten sample for doing quantile calculation along each image
sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
abs_sample = sample.abs() # "a certain percentile absolute pixel value"
s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
s = torch.clamp(
s, min=1,
max=self.config.sample_max_value) # When clamped to min=1, equivalent to standard clipping to [-1, 1]
s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0
sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s"
sample = sample.reshape(batch_size, channels, *remaining_dims)
sample = sample.to(dtype)
return sample
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
def _sigma_to_t(self, sigma, log_sigmas):
# get log sigma
log_sigma = np.log(np.maximum(sigma, 1e-10))
# get distribution
dists = log_sigma - log_sigmas[:, np.newaxis]
# get sigmas range
low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
high_idx = low_idx + 1
low = log_sigmas[low_idx]
high = log_sigmas[high_idx]
# interpolate sigmas
w = (low - log_sigma) / (low - high)
w = np.clip(w, 0, 1)
# transform interpolation to time range
t = (1 - w) * low_idx + w * high_idx
t = t.reshape(sigma.shape)
return t
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
def _sigma_to_alpha_sigma_t(self, sigma):
if self.config.use_flow_sigmas:
alpha_t = 1 - sigma
sigma_t = sigma
else:
alpha_t = 1 / ((sigma**2 + 1)**0.5)
sigma_t = sigma * alpha_t
return alpha_t, sigma_t
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
"""Constructs the noise schedule of Karras et al. (2022)."""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
sigma_min = self.config.sigma_min if hasattr(self.config, "sigma_min") else None
sigma_max = self.config.sigma_max if hasattr(self.config, "sigma_max") else None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
rho = 7.0 # 7.0 is the value used in the paper
ramp = np.linspace(0, 1, num_inference_steps)
min_inv_rho = sigma_min**(1 / rho)
max_inv_rho = sigma_max**(1 / rho)
sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho))**rho
return sigmas
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
"""Constructs an exponential noise schedule."""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
sigma_min = self.config.sigma_min if hasattr(self.config, "sigma_min") else None
sigma_max = self.config.sigma_max if hasattr(self.config, "sigma_max") else None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps))
return sigmas
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
def _convert_to_beta(self,
in_sigmas: torch.Tensor,
num_inference_steps: int,
alpha: float = 0.6,
beta: float = 0.6) -> torch.Tensor:
"""From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
sigma_min = self.config.sigma_min if hasattr(self.config, "sigma_min") else None
sigma_max = self.config.sigma_max if hasattr(self.config, "sigma_max") else None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
sigmas = np.array([
sigma_min + (ppf * (sigma_max - sigma_min)) for ppf in
[scipy.stats.beta.ppf(timestep, alpha, beta) for timestep in 1 - np.linspace(0, 1, num_inference_steps)]
])
return sigmas
def convert_model_output(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
r"""
Convert the model output to the corresponding type the UniPC algorithm needs.
Args:
model_output (`torch.Tensor`):
The direct output from the learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.Tensor`:
The converted model output.
"""
timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
if sample is None:
if len(args) > 1:
sample = args[1]
else:
raise ValueError("missing `sample` as a required keyword argument")
if timestep is not None:
deprecate(
"timesteps",
"1.0.0",
"Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
if self.predict_x0:
if self.config.prediction_type == "epsilon":
x0_pred = (sample - sigma_t * model_output) / alpha_t
elif self.config.prediction_type == "sample":
x0_pred = model_output
elif self.config.prediction_type == "v_prediction":
x0_pred = alpha_t * sample - sigma_t * model_output
elif self.config.prediction_type == "flow_prediction":
sigma_t = self.sigmas[self.step_index]
x0_pred = sample - sigma_t * model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, "
"`v_prediction`, or `flow_prediction` for the UniPCMultistepScheduler.")
if self.config.thresholding:
x0_pred = self._threshold_sample(x0_pred)
return x0_pred
else:
if self.config.prediction_type == "epsilon":
return model_output
elif self.config.prediction_type == "sample":
epsilon = (sample - alpha_t * model_output) / sigma_t
return epsilon
elif self.config.prediction_type == "v_prediction":
epsilon = alpha_t * model_output + sigma_t * sample
return epsilon
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction` for the UniPCMultistepScheduler.")
def multistep_uni_p_bh_update(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
order: int = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.
Args:
model_output (`torch.Tensor`):
The direct output from the learned diffusion model at the current timestep.
prev_timestep (`int`):
The previous discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
order (`int`):
The order of UniP at this timestep (corresponds to the *p* in UniPC-p).
Returns:
`torch.Tensor`:
The sample tensor at the previous timestep.
"""
prev_timestep = args[0] if len(args) > 0 else kwargs.pop("prev_timestep", None)
if sample is None:
if len(args) > 1:
sample = args[1]
else:
raise ValueError("missing `sample` as a required keyword argument")
if order is None:
if len(args) > 2:
order = args[2]
else:
raise ValueError("missing `order` as a required keyword argument")
if prev_timestep is not None:
deprecate(
"prev_timestep",
"1.0.0",
"Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
model_output_list = self.model_outputs
s0 = self.timestep_list[-1]
m0 = model_output_list[-1]
x = sample
if self.solver_p:
x_t = self.solver_p.step(model_output, s0, x).prev_sample
return x_t
sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
h = lambda_t - lambda_s0
device = sample.device
rks = []
D1s = []
for i in range(1, order):
si = self.step_index - i
mi = model_output_list[-(i + 1)]
alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
rk = (lambda_si - lambda_s0) / h
rks.append(rk)
D1s.append((mi - m0) / rk)
rks.append(1.0)
rks = torch.tensor(rks, device=device)
R = []
b = []
hh = -h if self.predict_x0 else h
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.config.solver_type == "bh1":
B_h = hh
elif self.config.solver_type == "bh2":
B_h = torch.expm1(hh)
else:
raise NotImplementedError()
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= i + 1
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=device)
if len(D1s) > 0:
D1s = torch.stack(D1s, dim=1) # (B, K)
# for order 2, we use a simplified version
if order == 2:
rhos_p = torch.tensor([0.5], dtype=x.dtype, device=device)
else:
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1]).to(device).to(x.dtype)
else:
D1s = None
if self.predict_x0:
x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s) if D1s is not None else 0
x_t = x_t_ - alpha_t * B_h * pred_res
else:
x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s) if D1s is not None else 0
x_t = x_t_ - sigma_t * B_h * pred_res
x_t = x_t.to(x.dtype)
return x_t
def multistep_uni_c_bh_update(
self,
this_model_output: torch.Tensor,
*args,
last_sample: torch.Tensor = None,
this_sample: torch.Tensor = None,
order: int = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the UniC (B(h) version).
Args:
this_model_output (`torch.Tensor`):
The model outputs at `x_t`.
this_timestep (`int`):
The current timestep `t`.
last_sample (`torch.Tensor`):
The generated sample before the last predictor `x_{t-1}`.
this_sample (`torch.Tensor`):
The generated sample after the last predictor `x_{t}`.
order (`int`):
The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.
Returns:
`torch.Tensor`:
The corrected sample tensor at the current timestep.
"""
this_timestep = args[0] if len(args) > 0 else kwargs.pop("this_timestep", None)
if last_sample is None:
if len(args) > 1:
last_sample = args[1]
else:
raise ValueError("missing `last_sample` as a required keyword argument")
if this_sample is None:
if len(args) > 2:
this_sample = args[2]
else:
raise ValueError("missing `this_sample` as a required keyword argument")
if order is None:
if len(args) > 3:
order = args[3]
else:
raise ValueError("missing `order` as a required keyword argument")
if this_timestep is not None:
deprecate(
"this_timestep",
"1.0.0",
"Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
model_output_list = self.model_outputs
m0 = model_output_list[-1]
x = last_sample
x_t = this_sample
model_t = this_model_output
sigma_t, sigma_s0 = self.sigmas[self.step_index], self.sigmas[self.step_index - 1]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
h = lambda_t - lambda_s0
device = this_sample.device
rks = []
D1s = []
for i in range(1, order):
si = self.step_index - (i + 1)
mi = model_output_list[-(i + 1)]
alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
rk = (lambda_si - lambda_s0) / h
rks.append(rk)
D1s.append((mi - m0) / rk)
rks.append(1.0)
rks = torch.tensor(rks, device=device)
R = []
b = []
hh = -h if self.predict_x0 else h
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.config.solver_type == "bh1":
B_h = hh
elif self.config.solver_type == "bh2":
B_h = torch.expm1(hh)
else:
raise NotImplementedError()
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= i + 1
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=device)
D1s = torch.stack(D1s, dim=1) if len(D1s) > 0 else None
# for order 1, we use a simplified version
if order == 1:
rhos_c = torch.tensor([0.5], dtype=x.dtype, device=device)
else:
rhos_c = torch.linalg.solve(R, b).to(device).to(x.dtype)
if self.predict_x0:
x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s) if D1s is not None else 0
D1_t = model_t - m0
x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
else:
x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s) if D1s is not None else 0
D1_t = model_t - m0
x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
x_t = x_t.to(x.dtype)
return x_t
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
index_candidates = (schedule_timesteps == timestep).nonzero()
if len(index_candidates) == 0:
step_index = len(self.timesteps) - 1
# The sigma index that is taken for the **very** first `step`
# is always the second index (or the last index if there is only 1)
# This way we can ensure we don't accidentally skip a sigma in
# case we start in the middle of the denoising schedule (e.g. for image-to-image)
elif len(index_candidates) > 1:
step_index = index_candidates[1].item()
else:
step_index = index_candidates[0].item()
return step_index
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
def _init_step_index(self, timestep):
"""
Initialize the step_index counter for the scheduler.
"""
if self.begin_index is None:
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
self._step_index = self.index_for_timestep(timestep)
else:
self._step_index = self._begin_index
def step(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor,
return_dict: bool = True,
) -> Union[SchedulerOutput, Tuple]:
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
the multistep UniPC.
Args:
model_output (`torch.Tensor`):
The direct output from learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
if self.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler")
if self.step_index is None:
self._init_step_index(timestep)
use_corrector = (self.step_index > 0 and self.step_index - 1 not in self.disable_corrector
and self.last_sample is not None)
model_output_convert = self.convert_model_output(model_output, sample=sample)
if use_corrector:
sample = self.multistep_uni_c_bh_update(
this_model_output=model_output_convert,
last_sample=self.last_sample,
this_sample=sample,
order=self.this_order,
)
for i in range(self.config.solver_order - 1):
self.model_outputs[i] = self.model_outputs[i + 1]
self.timestep_list[i] = self.timestep_list[i + 1]
self.model_outputs[-1] = model_output_convert
self.timestep_list[-1] = timestep
if self.config.lower_order_final:
this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
else:
this_order = self.config.solver_order
self.this_order = min(this_order, self.lower_order_nums + 1) # warmup for multistep
assert self.this_order > 0
self.last_sample = sample
prev_sample = self.multistep_uni_p_bh_update(
model_output=model_output, # pass the original non-converted model output, in case solver-p is used
sample=sample,
order=self.this_order,
)
if self.lower_order_nums < self.config.solver_order:
self.lower_order_nums += 1
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample, )
return SchedulerOutput(prev_sample=prev_sample)
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
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
def add_noise(
self,
original_samples: torch.Tensor,
noise: torch.Tensor,
timesteps: torch.IntTensor,
) -> torch.Tensor:
# Make sure sigmas and timesteps have the same device and dtype as original_samples
sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
# mps does not support float64
schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
else:
schedule_timesteps = self.timesteps.to(original_samples.device)
timesteps = timesteps.to(original_samples.device)
# begin_index is None when the 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 timesteps]
elif self.step_index is not None:
# add_noise is called after first denoising step (for inpainting)
step_indices = [self.step_index] * timesteps.shape[0]
else:
# add noise is called before first denoising step to create initial latent(img2img)
step_indices = [self.begin_index] * timesteps.shape[0]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(original_samples.shape):
sigma = sigma.unsqueeze(-1)
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
noisy_samples = alpha_t * original_samples + sigma_t * noise
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.step_index
step_index
The index counter for current timestep. It will increase 1 after each scheduler step.
Source
def step_index(self):
"""
The index counter for current timestep. It will increase 1 after each scheduler step.
"""
return self._step_index
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.begin_index
begin_index
The index for the first timestep. It should be set from pipeline with set_begin_index method.
Source
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
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.set_shift
set_shift(shift: float) -> None
Source
def set_shift(self, shift: float) -> None:
self.config.flow_shift = shift
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.set_begin_index
set_begin_index(begin_index: int = 0)
Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
Parameters
begin_index: `int`The begin index for the scheduler.
Source
def set_begin_index(self, begin_index: int = 0):
"""
Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
Args:
begin_index (`int`):
The begin index for the scheduler.
"""
self._begin_index = begin_index</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.set_timesteps
set_timesteps(num_inference_steps: int, device: Union[str, torch.device] = None, mu: Optional[float] = None)
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Parameters
num_inference_steps: `int`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.
Source
def set_timesteps(self,
num_inference_steps: int,
device: Union[str, torch.device] = None,
mu: Optional[float] = None):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
num_inference_steps (`int`):
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.
"""
# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://huggingface.co/papers/2305.08891
if mu is not None:
assert self.config.use_dynamic_shifting and self.config.time_shift_type == "exponential"
self.config.flow_shift = np.exp(mu)
if self.config.timestep_spacing == "linspace":
timesteps = (np.linspace(0, self.config.num_train_timesteps - 1,
num_inference_steps + 1).round()[::-1][:-1].copy().astype(np.int64))
elif self.config.timestep_spacing == "leading":
step_ratio = self.config.num_train_timesteps // (num_inference_steps + 1)
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64)
timesteps += self.config.steps_offset
elif self.config.timestep_spacing == "trailing":
step_ratio = self.config.num_train_timesteps / num_inference_steps
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = np.arange(self.config.num_train_timesteps, 0, -step_ratio).round().copy().astype(np.int64)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
)
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod)**0.5)
if self.config.use_karras_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_exponential_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_beta_sigmas:
log_sigmas = np.log(sigmas)
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
elif self.config.use_flow_sigmas:
alphas = np.linspace(1, 1 / self.config.num_train_timesteps, num_inference_steps + 1)
sigmas = 1.0 - alphas
sigmas = np.flip(self.config.flow_shift * sigmas / (1 + (self.config.flow_shift - 1) * sigmas))[:-1].copy()
timesteps = (sigmas * self.config.num_train_timesteps).copy()
if self.config.final_sigmas_type == "sigma_min":
sigma_last = sigmas[-1]
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
else:
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
if self.config.final_sigmas_type == "sigma_min":
sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0])**0.5
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
self.sigmas = torch.from_numpy(sigmas)
self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
self.num_inference_steps = len(timesteps)
self.model_outputs = [
None,
] * self.config.solver_order
self.lower_order_nums = 0
self.last_sample = None
if self.solver_p:
self.solver_p.set_timesteps(self.num_inference_steps, device=device)
# add an index counter for schedulers that allow duplicated timesteps
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.convert_model_output
convert_model_output(model_output: torch.Tensor, *args, sample: torch.Tensor = None, **kwargs) -> torch.Tensor
Convert the model output to the corresponding type the UniPC algorithm needs.
Parameters
model_output: `torch.Tensor`The direct output from the learned diffusion model.
timestep: `int`The current discrete timestep in the diffusion chain.
sample: `torch.Tensor`A current instance of a sample created by the diffusion process.
Returns
torch.Tensortorch.Tensor:
The converted model output.
Source
def convert_model_output(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
r"""
Convert the model output to the corresponding type the UniPC algorithm needs.
Args:
model_output (`torch.Tensor`):
The direct output from the learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.Tensor`:
The converted model output.
"""
timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
if sample is None:
if len(args) > 1:
sample = args[1]
else:
raise ValueError("missing `sample` as a required keyword argument")
if timestep is not None:
deprecate(
"timesteps",
"1.0.0",
"Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
if self.predict_x0:
if self.config.prediction_type == "epsilon":
x0_pred = (sample - sigma_t * model_output) / alpha_t
elif self.config.prediction_type == "sample":
x0_pred = model_output
elif self.config.prediction_type == "v_prediction":
x0_pred = alpha_t * sample - sigma_t * model_output
elif self.config.prediction_type == "flow_prediction":
sigma_t = self.sigmas[self.step_index]
x0_pred = sample - sigma_t * model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, "
"`v_prediction`, or `flow_prediction` for the UniPCMultistepScheduler.")
if self.config.thresholding:
x0_pred = self._threshold_sample(x0_pred)
return x0_pred
else:
if self.config.prediction_type == "epsilon":
return model_output
elif self.config.prediction_type == "sample":
epsilon = (sample - alpha_t * model_output) / sigma_t
return epsilon
elif self.config.prediction_type == "v_prediction":
epsilon = alpha_t * model_output + sigma_t * sample
return epsilon
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction` for the UniPCMultistepScheduler.")</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.multistep_uni_p_bh_update
multistep_uni_p_bh_update(model_output: torch.Tensor, *args, sample: torch.Tensor = None, order: int = None, **kwargs) -> torch.Tensor
One step for the UniP (B(h) version). Alternatively, self.solver_p is used if is specified.
Parameters
model_output: `torch.Tensor`The direct output from the learned diffusion model at the current timestep.
prev_timestep: `int`The previous discrete timestep in the diffusion chain.
sample: `torch.Tensor`A current instance of a sample created by the diffusion process.
order: `int`The order of UniP at this timestep (corresponds to the p in UniPC-p).
Returns
torch.Tensortorch.Tensor:
The sample tensor at the previous timestep.
Source
def multistep_uni_p_bh_update(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
order: int = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.
Args:
model_output (`torch.Tensor`):
The direct output from the learned diffusion model at the current timestep.
prev_timestep (`int`):
The previous discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
order (`int`):
The order of UniP at this timestep (corresponds to the *p* in UniPC-p).
Returns:
`torch.Tensor`:
The sample tensor at the previous timestep.
"""
prev_timestep = args[0] if len(args) > 0 else kwargs.pop("prev_timestep", None)
if sample is None:
if len(args) > 1:
sample = args[1]
else:
raise ValueError("missing `sample` as a required keyword argument")
if order is None:
if len(args) > 2:
order = args[2]
else:
raise ValueError("missing `order` as a required keyword argument")
if prev_timestep is not None:
deprecate(
"prev_timestep",
"1.0.0",
"Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
model_output_list = self.model_outputs
s0 = self.timestep_list[-1]
m0 = model_output_list[-1]
x = sample
if self.solver_p:
x_t = self.solver_p.step(model_output, s0, x).prev_sample
return x_t
sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
h = lambda_t - lambda_s0
device = sample.device
rks = []
D1s = []
for i in range(1, order):
si = self.step_index - i
mi = model_output_list[-(i + 1)]
alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
rk = (lambda_si - lambda_s0) / h
rks.append(rk)
D1s.append((mi - m0) / rk)
rks.append(1.0)
rks = torch.tensor(rks, device=device)
R = []
b = []
hh = -h if self.predict_x0 else h
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.config.solver_type == "bh1":
B_h = hh
elif self.config.solver_type == "bh2":
B_h = torch.expm1(hh)
else:
raise NotImplementedError()
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= i + 1
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=device)
if len(D1s) > 0:
D1s = torch.stack(D1s, dim=1) # (B, K)
# for order 2, we use a simplified version
if order == 2:
rhos_p = torch.tensor([0.5], dtype=x.dtype, device=device)
else:
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1]).to(device).to(x.dtype)
else:
D1s = None
if self.predict_x0:
x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s) if D1s is not None else 0
x_t = x_t_ - alpha_t * B_h * pred_res
else:
x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
pred_res = torch.einsum("k,bkc...->bc...", rhos_p, D1s) if D1s is not None else 0
x_t = x_t_ - sigma_t * B_h * pred_res
x_t = x_t.to(x.dtype)
return x_t</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.multistep_uni_c_bh_update
multistep_uni_c_bh_update(this_model_output: torch.Tensor, *args, last_sample: torch.Tensor = None, this_sample: torch.Tensor = None, order: int = None, **kwargs) -> torch.Tensor
One step for the UniC (B(h) version).
Parameters
this_model_output: `torch.Tensor`The model outputs at x_t.
this_timestep: `int`The current timestep t.
last_sample: `torch.Tensor`The generated sample before the last predictor x_{t-1}.
this_sample: `torch.Tensor`The generated sample after the last predictor x_{t}.
order: `int`The p of UniC-p at this step. The effective order of accuracy should be order + 1.
Returns
torch.Tensortorch.Tensor:
The corrected sample tensor at the current timestep.
Source
def multistep_uni_c_bh_update(
self,
this_model_output: torch.Tensor,
*args,
last_sample: torch.Tensor = None,
this_sample: torch.Tensor = None,
order: int = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the UniC (B(h) version).
Args:
this_model_output (`torch.Tensor`):
The model outputs at `x_t`.
this_timestep (`int`):
The current timestep `t`.
last_sample (`torch.Tensor`):
The generated sample before the last predictor `x_{t-1}`.
this_sample (`torch.Tensor`):
The generated sample after the last predictor `x_{t}`.
order (`int`):
The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.
Returns:
`torch.Tensor`:
The corrected sample tensor at the current timestep.
"""
this_timestep = args[0] if len(args) > 0 else kwargs.pop("this_timestep", None)
if last_sample is None:
if len(args) > 1:
last_sample = args[1]
else:
raise ValueError("missing `last_sample` as a required keyword argument")
if this_sample is None:
if len(args) > 2:
this_sample = args[2]
else:
raise ValueError("missing `this_sample` as a required keyword argument")
if order is None:
if len(args) > 3:
order = args[3]
else:
raise ValueError("missing `order` as a required keyword argument")
if this_timestep is not None:
deprecate(
"this_timestep",
"1.0.0",
"Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
model_output_list = self.model_outputs
m0 = model_output_list[-1]
x = last_sample
x_t = this_sample
model_t = this_model_output
sigma_t, sigma_s0 = self.sigmas[self.step_index], self.sigmas[self.step_index - 1]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
h = lambda_t - lambda_s0
device = this_sample.device
rks = []
D1s = []
for i in range(1, order):
si = self.step_index - (i + 1)
mi = model_output_list[-(i + 1)]
alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
rk = (lambda_si - lambda_s0) / h
rks.append(rk)
D1s.append((mi - m0) / rk)
rks.append(1.0)
rks = torch.tensor(rks, device=device)
R = []
b = []
hh = -h if self.predict_x0 else h
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.config.solver_type == "bh1":
B_h = hh
elif self.config.solver_type == "bh2":
B_h = torch.expm1(hh)
else:
raise NotImplementedError()
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= i + 1
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=device)
D1s = torch.stack(D1s, dim=1) if len(D1s) > 0 else None
# for order 1, we use a simplified version
if order == 1:
rhos_c = torch.tensor([0.5], dtype=x.dtype, device=device)
else:
rhos_c = torch.linalg.solve(R, b).to(device).to(x.dtype)
if self.predict_x0:
x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s) if D1s is not None else 0
D1_t = model_t - m0
x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
else:
x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
corr_res = torch.einsum("k,bkc...->bc...", rhos_c[:-1], D1s) if D1s is not None else 0
D1_t = model_t - m0
x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
x_t = x_t.to(x.dtype)
return x_t</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.index_for_timestep
index_for_timestep(timestep, schedule_timesteps = None)
Source
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
index_candidates = (schedule_timesteps == timestep).nonzero()
if len(index_candidates) == 0:
step_index = len(self.timesteps) - 1
# The sigma index that is taken for the **very** first `step`
# is always the second index (or the last index if there is only 1)
# This way we can ensure we don't accidentally skip a sigma in
# case we start in the middle of the denoising schedule (e.g. for image-to-image)
elif len(index_candidates) > 1:
step_index = index_candidates[1].item()
else:
step_index = index_candidates[0].item()
return step_index</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.step
step(model_output: torch.Tensor, timestep: Union[int, torch.Tensor], sample: torch.Tensor, return_dict: bool = True) -> Union[SchedulerOutput, Tuple]
Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
the multistep UniPC.
Parameters
model_output: `torch.Tensor`The direct output from learned diffusion model.
timestep: `int`The current discrete timestep in the diffusion chain.
sample: `torch.Tensor`A current instance of a sample created by the diffusion process.
return_dict: `bool`Whether or not to return a [~schedulers.scheduling_utils.SchedulerOutput] or tuple.
Returns
Union[SchedulerOutput, Tuple][~schedulers.scheduling_utils.SchedulerOutput] or tuple:
If return_dict is True, [~schedulers.scheduling_utils.SchedulerOutput] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
Source
def step(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor,
return_dict: bool = True,
) -> Union[SchedulerOutput, Tuple]:
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
the multistep UniPC.
Args:
model_output (`torch.Tensor`):
The direct output from learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
if self.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler")
if self.step_index is None:
self._init_step_index(timestep)
use_corrector = (self.step_index > 0 and self.step_index - 1 not in self.disable_corrector
and self.last_sample is not None)
model_output_convert = self.convert_model_output(model_output, sample=sample)
if use_corrector:
sample = self.multistep_uni_c_bh_update(
this_model_output=model_output_convert,
last_sample=self.last_sample,
this_sample=sample,
order=self.this_order,
)
for i in range(self.config.solver_order - 1):
self.model_outputs[i] = self.model_outputs[i + 1]
self.timestep_list[i] = self.timestep_list[i + 1]
self.model_outputs[-1] = model_output_convert
self.timestep_list[-1] = timestep
if self.config.lower_order_final:
this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
else:
this_order = self.config.solver_order
self.this_order = min(this_order, self.lower_order_nums + 1) # warmup for multistep
assert self.this_order > 0
self.last_sample = sample
prev_sample = self.multistep_uni_p_bh_update(
model_output=model_output, # pass the original non-converted model output, in case solver-p is used
sample=sample,
order=self.this_order,
)
if self.lower_order_nums < self.config.solver_order:
self.lower_order_nums += 1
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample, )
return SchedulerOutput(prev_sample=prev_sample)</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.scale_model_input
scale_model_input(sample: torch.Tensor, *args, **kwargs) -> torch.Tensor
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Parameters
sample: `torch.Tensor`The input sample.
Returns
torch.Tensortorch.Tensor:
A scaled input sample.
Source
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</code></pre></details>
fastvideo.models.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler.add_noise
add_noise(original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor
Source
def add_noise(
self,
original_samples: torch.Tensor,
noise: torch.Tensor,
timesteps: torch.IntTensor,
) -> torch.Tensor:
# Make sure sigmas and timesteps have the same device and dtype as original_samples
sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
# mps does not support float64
schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
else:
schedule_timesteps = self.timesteps.to(original_samples.device)
timesteps = timesteps.to(original_samples.device)
# begin_index is None when the 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 timesteps]
elif self.step_index is not None:
# add_noise is called after first denoising step (for inpainting)
step_indices = [self.step_index] * timesteps.shape[0]
else:
# add noise is called before first denoising step to create initial latent(img2img)
step_indices = [self.begin_index] * timesteps.shape[0]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(original_samples.shape):
sigma = sigma.unsqueeze(-1)
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
noisy_samples = alpha_t * original_samples + sigma_t * noise
return noisy_samples</code></pre></details>