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import math
import torch
import numpy as np
def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):
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(t2) / alpha_bar(t1), max_beta))
return np.array(betas)
def make_beta_schedule(schedule, n_timestep, linear_start=1e-4, linear_end=2e-2, cosine_s=8e-3):
if schedule == "linear":
betas = (
torch.linspace(linear_start ** 0.5, linear_end ** 0.5, n_timestep, dtype=torch.float64) ** 2
)
elif schedule == "cosine":
timesteps = (
torch.arange(n_timestep + 1, dtype=torch.float64) / n_timestep + cosine_s
)
alphas = timesteps / (1 + cosine_s) * np.pi / 2
alphas = torch.cos(alphas).pow(2)
alphas = alphas / alphas[0]
betas = 1 - alphas[1:] / alphas[:-1]
betas = torch.clamp(betas, min=0, max=0.999)
elif schedule == "sqrt_linear":
betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64)
elif schedule == "sqrt":
betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64) ** 0.5
else:
raise ValueError(f"schedule '{schedule}' unknown.")
return betas
def time_snr_shift(alpha, t):
if alpha == 1.0:
return t
return alpha * t / (1 + (alpha - 1) * t)
def flux_time_shift(mu, sigma, t):
return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)
class AbstractPrediction(torch.nn.Module):
def __init__(self, sigma_data=1.0, prediction_type='epsilon'):
super().__init__()
self.sigma_data = sigma_data
self.prediction_type = prediction_type
assert self.prediction_type in ['epsilon', 'const', 'v_prediction', 'edm']
def calculate_input(self, sigma, noise):
if self.prediction_type == 'const':
return noise
else:
sigma = sigma.view(sigma.shape[:1] + (1,) * (noise.ndim - 1))
return noise / (sigma ** 2 + self.sigma_data ** 2) ** 0.5
def calculate_denoised(self, sigma, model_output, model_input):
sigma = sigma.view(sigma.shape[:1] + (1,) * (model_output.ndim - 1))
if self.prediction_type == 'v_prediction':
return model_input * self.sigma_data ** 2 / (
sigma ** 2 + self.sigma_data ** 2) - model_output * sigma * self.sigma_data / (
sigma ** 2 + self.sigma_data ** 2) ** 0.5
elif self.prediction_type == 'edm':
return model_input * self.sigma_data ** 2 / (
sigma ** 2 + self.sigma_data ** 2) + model_output * sigma * self.sigma_data / (
sigma ** 2 + self.sigma_data ** 2) ** 0.5
else:
return model_input - model_output * sigma
def noise_scaling(self, sigma, noise, latent_image, max_denoise=False):
if self.prediction_type == 'const':
return sigma * noise + (1.0 - sigma) * latent_image
else:
if max_denoise:
noise = noise * torch.sqrt(1.0 + sigma ** 2.0)
else:
noise = noise * sigma
noise += latent_image
return noise
def inverse_noise_scaling(self, sigma, latent):
if self.prediction_type == 'const':
return latent / (1.0 - sigma)
else:
return latent
class Prediction(AbstractPrediction):
def __init__(self, sigma_data=1.0, prediction_type='eps', beta_schedule='linear', linear_start=0.00085,
linear_end=0.012, timesteps=1000):
super().__init__(sigma_data=sigma_data, prediction_type=prediction_type)
self.register_schedule(given_betas=None, beta_schedule=beta_schedule, timesteps=timesteps,
linear_start=linear_start, linear_end=linear_end, cosine_s=8e-3)
def register_schedule(self, given_betas=None, beta_schedule="linear", timesteps=1000,
linear_start=1e-4, linear_end=2e-2, cosine_s=8e-3):
if given_betas is not None:
betas = given_betas
else:
betas = make_beta_schedule(beta_schedule, timesteps, linear_start=linear_start, linear_end=linear_end,
cosine_s=cosine_s)
alphas = 1. - betas
alphas_cumprod = torch.cumprod(alphas, dim=0)
sigmas = ((1 - alphas_cumprod) / alphas_cumprod) ** 0.5
self.register_buffer('alphas_cumprod', alphas_cumprod.float())
self.register_buffer('sigmas', sigmas.float())
self.register_buffer('log_sigmas', sigmas.log().float())
return
@property
def sigma_min(self):
return self.sigmas[0]
@property
def sigma_max(self):
return self.sigmas[-1]
def timestep(self, sigma):
log_sigma = sigma.log()
dists = log_sigma.to(self.log_sigmas.device) - self.log_sigmas[:, None]
return dists.abs().argmin(dim=0).view(sigma.shape).to(sigma.device)
def sigma(self, timestep):
t = torch.clamp(timestep.float().to(self.log_sigmas.device), min=0, max=(len(self.sigmas) - 1))
low_idx = t.floor().long()
high_idx = t.ceil().long()
w = t.frac()
log_sigma = (1 - w) * self.log_sigmas[low_idx] + w * self.log_sigmas[high_idx]
return log_sigma.exp().to(timestep.device)
def percent_to_sigma(self, percent):
if percent <= 0.0:
return 999999999.9
if percent >= 1.0:
return 0.0
percent = 1.0 - percent
return self.sigma(torch.tensor(percent * 999.0)).item()
class PredictionEDM(Prediction):
def timestep(self, sigma):
return 0.25 * sigma.log()
def sigma(self, timestep):
return (timestep / 0.25).exp()
class PredictionContinuousEDM(AbstractPrediction):
def __init__(self, sigma_data=1.0, prediction_type='eps', sigma_min=0.002, sigma_max=120.0):
super().__init__(sigma_data=sigma_data, prediction_type=prediction_type)
self.set_parameters(sigma_min, sigma_max, sigma_data)
def set_parameters(self, sigma_min, sigma_max, sigma_data):
self.sigma_data = sigma_data
sigmas = torch.linspace(math.log(sigma_min), math.log(sigma_max), 1000).exp()
self.register_buffer('sigmas', sigmas)
self.register_buffer('log_sigmas', sigmas.log())
@property
def sigma_min(self):
return self.sigmas[0]
@property
def sigma_max(self):
return self.sigmas[-1]
def timestep(self, sigma):
return 0.25 * sigma.log()
def sigma(self, timestep):
return (timestep / 0.25).exp()
def percent_to_sigma(self, percent):
if percent <= 0.0:
return 999999999.9
if percent >= 1.0:
return 0.0
percent = 1.0 - percent
log_sigma_min = math.log(self.sigma_min)
return math.exp((math.log(self.sigma_max) - log_sigma_min) * percent + log_sigma_min)
class PredictionContinuousV(PredictionContinuousEDM):
def timestep(self, sigma):
return sigma.atan() / math.pi * 2
def sigma(self, timestep):
return (timestep * math.pi / 2).tan()
class PredictionFlow(AbstractPrediction):
def __init__(self, sigma_data=1.0, prediction_type='eps', shift=1.0, multiplier=1000, timesteps=1000):
super().__init__(sigma_data=sigma_data, prediction_type=prediction_type)
self.shift = shift
self.multiplier = multiplier
ts = self.sigma((torch.arange(1, timesteps + 1, 1) / timesteps) * multiplier)
self.register_buffer('sigmas', ts)
@property
def sigma_min(self):
return self.sigmas[0]
@property
def sigma_max(self):
return self.sigmas[-1]
def timestep(self, sigma):
return sigma * self.multiplier
def sigma(self, timestep):
return time_snr_shift(self.shift, timestep / self.multiplier)
def percent_to_sigma(self, percent):
if percent <= 0.0:
return 1.0
if percent >= 1.0:
return 0.0
return 1.0 - percent
class PredictionFlux(AbstractPrediction):
def __init__(self, sigma_data=1.0, prediction_type='const', shift=1.15, timesteps=10000):
super().__init__(sigma_data=sigma_data, prediction_type=prediction_type)
self.shift = shift
ts = self.sigma((torch.arange(1, timesteps + 1, 1) / timesteps))
self.register_buffer('sigmas', ts)
@property
def sigma_min(self):
return self.sigmas[0]
@property
def sigma_max(self):
return self.sigmas[-1]
def timestep(self, sigma):
return sigma
def sigma(self, timestep):
return flux_time_shift(self.shift, 1.0, timestep)
def percent_to_sigma(self, percent):
if percent <= 0.0:
return 1.0
if percent >= 1.0:
return 0.0
return 1.0 - percent
def k_prediction_from_diffusers_scheduler(scheduler):
if hasattr(scheduler.config, 'prediction_type') and scheduler.config.prediction_type in ["epsilon", "v_prediction"]:
if scheduler.config.beta_schedule == "scaled_linear":
return Prediction(sigma_data=1.0, prediction_type=scheduler.config.prediction_type, beta_schedule='linear',
linear_start=scheduler.config.beta_start, linear_end=scheduler.config.beta_end,
timesteps=scheduler.config.num_train_timesteps)
raise NotImplementedError(f'Failed to recognize {scheduler}')
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