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import torch
import numpy as np
class AbstractDistribution:
def sample(self):
raise NotImplementedError()
def mode(self):
raise NotImplementedError()
class DiracDistribution(AbstractDistribution):
def __init__(self, value):
self.value = value
def sample(self):
return self.value
def mode(self):
return self.value
class DiagonalGaussianDistribution(object):
def __init__(self, parameters, deterministic=False):
"""
parameters: input is expected to be a 2D tensor, where the first
half of the last dimension are the means and the second
half are the log-variances.
deterministic: if set to True, would mean that there is no randomness in the distribution
(i.e., variance and standard deviation are set to zero).
mathematical:
self.mean = µ
self.std = σ
self.var = σ^2
self.logvar = log(σ^2) = 2log(σ)
The logarithm of the variance (self.logvar) is also often used in formulas
in statistics. For example, the log-likelihood of a Gaussian distribution
involves the log of the variance. Therefore, working directly with the log
-variance can make the formulas simpler and more numerically stable.
"""
self.parameters = parameters
self.mean, self.logvar = torch.chunk(parameters, 2, dim=1)
self.logvar = torch.clamp(self.logvar, -30.0, 20.0)
self.deterministic = deterministic
self.std = torch.exp(0.5 * self.logvar)
self.var = torch.exp(self.logvar)
if self.deterministic:
self.var = self.std = torch.zeros_like(self.mean).to(device=self.parameters.device)
def sample(self):
"""
Reparameterization:
if Z is a standard normal random variable (i.e., Gaussian distributed
with mean 0 and standard deviation 1), X = μ + σZ is a normal random
variable with mean μ and standard deviation σ.
"""
x = self.mean + self.std * torch.randn(self.mean.shape).to(device=self.parameters.device)
return x
def kl(self, other=None):
"""
This function is to compute the KL-divergence of the current
Gaussian distribution with another one. If other is None, then
compute the KL-divergence with a standard distribution.
$ KL(P||Q) = log(σ_2 / σ_1) + \frac{σ_1^2 + (μ1 - μ2)^2}{2σ_2^2} - 0.5 $
"""
if self.deterministic:
return torch.Tensor([0.])
else:
if other is None:
return 0.5 * torch.sum(torch.pow(self.mean, 2)
+ self.var - 1.0 - self.logvar,
dim=[1, 2, 3])
else:
return 0.5 * torch.sum(
torch.pow(self.mean - other.mean, 2) / other.var
+ self.var / other.var - 1.0 - self.logvar + other.logvar,
dim=[1, 2, 3])
def nll(self, sample, dims=[1, 2, 3]):
"""
The negative log likelihood (NLL) of observing a sample x from a normal
distribution with mean μ and variance σ^2 is given by:
NLL = 0.5 * log(2πσ^2) + (1 / 2σ^2) * (x - μ)^2
"""
if self.deterministic:
return torch.Tensor([0.])
logtwopi = np.log(2.0 * np.pi)
return 0.5 * torch.sum(
logtwopi + self.logvar + torch.pow(sample - self.mean, 2) / self.var,
dim=dims)
def mode(self):
return self.mean
def normal_kl(mean1, logvar1, mean2, logvar2):
"""
source: https://github.com/openai/guided-diffusion/blob/27c20a8fab9cb472df5d6bdd6c8d11c8f430b924/guided_diffusion/losses.py#L12
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, torch.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 torch.exp().
logvar1, logvar2 = [
x if isinstance(x, torch.Tensor) else torch.tensor(x).to(tensor)
for x in (logvar1, logvar2)
]
return 0.5 * (
-1.0
+ logvar2
- logvar1
+ torch.exp(logvar1 - logvar2)
+ ((mean1 - mean2) ** 2) * torch.exp(-logvar2)
)
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