Why should lvlb_weights be implemented like this when parameterized as "x0"

[HWH-2019]

I don't understand why this is implemented like this:

  if self.parameterization == "eps":
      lvlb_weights = self.betas ** 2 / (
              2 * self.posterior_variance * to_torch(alphas) * (1 - self.alphas_cumprod))
  elif self.parameterization == "x0":
      lvlb_weights = 0.5 * np.sqrt(torch.Tensor(alphas_cumprod)) / (2. * 1 - torch.Tensor(alphas_cumprod)) # Confusing
  else:
      raise NotImplementedError("mu not supported")

I think it should be implemented like this:

I want to add parameterization as "v", how can I modify the code, divide by alpha squared, or whatever

[houjie8888]

I have the same problem, may I know if it has been resolved?

[HWH-2019]

I have the same problem, may I know if it has been resolved?

Sorry, I haven't solved this problem yet, wait for the someone to explain

[kliyer-ai]

You can find the v parameterization here @HWH-2019 https://github.com/Stability-AI/stablediffusion/blob/main/ldm/models/diffusion/ddpm.py#L896

[liuchangzong]

I even don't know why lvlb_weight should be written like this,. Could you please tell me why? Maybe a link or a paper which describes lvlb equation will be helpful. Thanks a lot!

[tyxsspa]

any one can explain lvlb_weight? thanks

[ytoon]

This refers to equation(12) in https://arxiv.org/abs/2006.11239v2.