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"""
Helpers for various likelihood-based losses. These are ported from the original
Ho et al. diffusion models codebase:
https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/utils.py
"""
import numpy as np
import torch as th
def normal_kl(mean1, logvar1, mean2, logvar2):
"""
Compute the KL divergence between two gaussians.
Shapes are automatically broadcasted, so batches can be compared to
scalars, among other use cases.
"""
tensor = None
for obj in (mean1, logvar1, mean2, logvar2):
if isinstance(obj, th.Tensor):
tensor = obj
break
assert tensor is not None, "at least one argument must be a Tensor"
# Force variances to be Tensors. Broadcasting helps convert scalars to
# Tensors, but it does not work for th.exp().
logvar1, logvar2 = [
x if isinstance(x, th.Tensor) else th.tensor(x).to(tensor)
for x in (logvar1, logvar2)
]
# print(logvar2.shape)
# temp1 = 0.5 * (-1.0 + logvar2 - logvar1 + th.exp(logvar1 - logvar2))
# print(f'const = {temp1.mean()}, coef={(th.exp(-logvar2) * 0.5).mean()}, mse={((mean1 - mean2) ** 2).mean().item()}')
return 0.5 * (
-1.0
+ logvar2
- logvar1
+ th.exp(logvar1 - logvar2)
+ ((mean1 - mean2) ** 2) * th.exp(-logvar2)
)
def approx_standard_normal_cdf(x):
"""
A fast approximation of the cumulative distribution function of the
standard normal.
"""
return 0.5 * (1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3))))
def discretized_gaussian_log_likelihood(x, *, means, log_scales):
"""
Compute the log-likelihood of a Gaussian distribution discretizing to a
given image.
:param x: the target images. It is assumed that this was uint8 values,
rescaled to the range [-1, 1].
:param means: the Gaussian mean Tensor.
:param log_scales: the Gaussian log stddev Tensor.
:return: a tensor like x of log probabilities (in nats).
"""
assert x.shape == means.shape == log_scales.shape
centered_x = x - means
inv_stdv = th.exp(-log_scales)
plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
cdf_plus = approx_standard_normal_cdf(plus_in)
min_in = inv_stdv * (centered_x - 1.0 / 255.0)
cdf_min = approx_standard_normal_cdf(min_in)
log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
cdf_delta = cdf_plus - cdf_min
log_probs = th.where(
x < -0.999,
log_cdf_plus,
th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))),
)
assert log_probs.shape == x.shape
return log_probs
def gaussian_density(x, *, means, log_scales):
from torch.distributions import Normal
normal_dist = Normal(means, log_scales.exp())
logp = normal_dist.log_prob(x)
return logp
def discretized_text_log_likelihood(x, *, means, log_scales):
"""
Compute the log-likelihood of a Gaussian distribution discretizing to a
given image.
:param x: the target images. It is assumed that this was uint8 values,
rescaled to the range [-1, 1].
:param means: the Gaussian mean Tensor.
:param log_scales: the Gaussian log stddev Tensor.
:return: a tensor like x of log probabilities (in nats).
"""
print(x.shape, means.shape)
# assert x.shape == means.shape == log_scales.shape
print(x, means)
centered_x = x - means
inv_stdv = th.exp(-log_scales)
plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
cdf_plus = approx_standard_normal_cdf(plus_in)
min_in = inv_stdv * (centered_x - 1.0 / 255.0)
cdf_min = approx_standard_normal_cdf(min_in)
log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
cdf_delta = cdf_plus - cdf_min
log_probs = th.where(
x < -0.999,
log_cdf_plus,
th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))),
)
assert log_probs.shape == x.shape
return log_probs
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