content: 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):
          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):
          x = self.mean + self.std * torch.randn(self.mean.shape).to(device=self.parameters.device)
          return x
  
      def kl(self, other=None):
          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]):
          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)
      )
  