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import torch
from scipy import integrate
from ...util import append_dims
def linear_multistep_coeff(order, t, i, j, epsrel=1e-4):
if order - 1 > i:
raise ValueError(f"Order {order} too high for step {i}")
def fn(tau):
prod = 1.0
for k in range(order):
if j == k:
continue
prod *= (tau - t[i - k]) / (t[i - j] - t[i - k])
return prod
return integrate.quad(fn, t[i], t[i + 1], epsrel=epsrel)[0]
def get_ancestral_step(sigma_from, sigma_to, eta=1.0):
if not eta:
return sigma_to, 0.0
sigma_up = torch.minimum(
sigma_to,
eta
* (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5,
)
sigma_down = (sigma_to**2 - sigma_up**2) ** 0.5
return sigma_down, sigma_up
def to_d(x, sigma, denoised):
return (x - denoised) / append_dims(sigma, x.ndim)
def to_neg_log_sigma(sigma):
return sigma.log().neg()
def to_sigma(neg_log_sigma):
return neg_log_sigma.neg().exp()
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