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import torch |
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import numpy as np |
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class AbstractDistribution: |
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def sample(self): |
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raise NotImplementedError() |
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def mode(self): |
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raise NotImplementedError() |
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class DiracDistribution(AbstractDistribution): |
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def __init__(self, value): |
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self.value = value |
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def sample(self): |
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return self.value |
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def mode(self): |
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return self.value |
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class DiagonalGaussianDistribution(object): |
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def __init__(self, parameters, deterministic=False): |
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""" |
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parameters: input is expected to be a 2D tensor, where the first |
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half of the last dimension are the means and the second |
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half are the log-variances. |
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deterministic: if set to True, would mean that there is no randomness in the distribution |
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(i.e., variance and standard deviation are set to zero). |
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mathematical: |
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self.mean = µ |
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self.std = σ |
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self.var = σ^2 |
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self.logvar = log(σ^2) = 2log(σ) |
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The logarithm of the variance (self.logvar) is also often used in formulas |
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in statistics. For example, the log-likelihood of a Gaussian distribution |
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involves the log of the variance. Therefore, working directly with the log |
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-variance can make the formulas simpler and more numerically stable. |
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""" |
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self.parameters = parameters |
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self.mean, self.logvar = torch.chunk(parameters, 2, dim=1) |
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self.logvar = torch.clamp(self.logvar, -30.0, 20.0) |
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self.deterministic = deterministic |
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self.std = torch.exp(0.5 * self.logvar) |
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self.var = torch.exp(self.logvar) |
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if self.deterministic: |
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self.var = self.std = torch.zeros_like(self.mean).to(device=self.parameters.device) |
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def sample(self): |
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""" |
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Reparameterization: |
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if Z is a standard normal random variable (i.e., Gaussian distributed |
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with mean 0 and standard deviation 1), X = μ + σZ is a normal random |
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variable with mean μ and standard deviation σ. |
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""" |
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x = self.mean + self.std * torch.randn(self.mean.shape).to(device=self.parameters.device) |
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return x |
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def kl(self, other=None): |
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""" |
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This function is to compute the KL-divergence of the current |
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Gaussian distribution with another one. If other is None, then |
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compute the KL-divergence with a standard distribution. |
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$ KL(P||Q) = log(σ_2 / σ_1) + \frac{σ_1^2 + (μ1 - μ2)^2}{2σ_2^2} - 0.5 $ |
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""" |
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if self.deterministic: |
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return torch.Tensor([0.]) |
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else: |
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if other is None: |
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return 0.5 * torch.sum(torch.pow(self.mean, 2) |
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+ self.var - 1.0 - self.logvar, |
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dim=[1, 2, 3]) |
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else: |
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return 0.5 * torch.sum( |
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torch.pow(self.mean - other.mean, 2) / other.var |
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+ self.var / other.var - 1.0 - self.logvar + other.logvar, |
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dim=[1, 2, 3]) |
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def nll(self, sample, dims=[1, 2, 3]): |
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""" |
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The negative log likelihood (NLL) of observing a sample x from a normal |
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distribution with mean μ and variance σ^2 is given by: |
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NLL = 0.5 * log(2πσ^2) + (1 / 2σ^2) * (x - μ)^2 |
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""" |
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if self.deterministic: |
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return torch.Tensor([0.]) |
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logtwopi = np.log(2.0 * np.pi) |
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return 0.5 * torch.sum( |
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logtwopi + self.logvar + torch.pow(sample - self.mean, 2) / self.var, |
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dim=dims) |
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def mode(self): |
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return self.mean |
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def normal_kl(mean1, logvar1, mean2, logvar2): |
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""" |
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source: https://github.com/openai/guided-diffusion/blob/27c20a8fab9cb472df5d6bdd6c8d11c8f430b924/guided_diffusion/losses.py#L12 |
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Compute the KL divergence between two Gaussians. |
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Shapes are automatically broadcasted, so batches can be compared to |
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scalars, among other use cases. |
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""" |
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tensor = None |
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for obj in (mean1, logvar1, mean2, logvar2): |
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if isinstance(obj, torch.Tensor): |
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tensor = obj |
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break |
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assert tensor is not None, "at least one argument must be a Tensor" |
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logvar1, logvar2 = [ |
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x if isinstance(x, torch.Tensor) else torch.tensor(x).to(tensor) |
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for x in (logvar1, logvar2) |
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] |
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return 0.5 * ( |
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-1.0 |
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+ logvar2 |
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- logvar1 |
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+ torch.exp(logvar1 - logvar2) |
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+ ((mean1 - mean2) ** 2) * torch.exp(-logvar2) |
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) |
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