Question about Eq. (4) and VP SDE implementation

[SuwoongHeo]

Hi,

In the paper, the sampling equation of VP SDE (=: DDPM) differs from the DDPM's form. Specifically, the multiplicand to the score function is defined as $\beta_i$ while DDPM uses $(1-\alpha_t)/(\sqrt{1-\bar{\alpha_t}})$. It seems that the code in the repo originally intended to use $\bar{\alpha_t}$ since it is initialized (but not used) as can be seen in the below snippet. Can you provide me reason for this difference?

score_sde_pytorch/sde_lib.py

Line 127 in cb1f359

self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)

[prithuls]

Hi, I am just starting to work on this repo code. I noticed the authors defined different loss functions. If we are to use DDPM loss function, we would need self.alphas_cumprod that you mentioned. If you check the following lines, i.e.

score_sde_pytorch/losses.py

Line 138 in cb1f359

sqrt_1m_alphas_cumprod = vpsde.sqrt_1m_alphas_cumprod.to(batch.device)

This self.sqrt_1m_alphas_cumprod has been later used in losses.py to get DDPM loss function i.e.

score_sde_pytorch/losses.py

Line 138 in cb1f359

sqrt_1m_alphas_cumprod = vpsde.sqrt_1m_alphas_cumprod.to(batch.device)

.

P.S. I am not sure why the loss SDE function is that way though.