Questions about Eq. 13

[ArlenCHEN]

Dear authors,

Thanks for the brilliant work!

I still have some confusion about the Eq. 13, although I have read discussions in previous issues.

You mentioned in the suppplementary that:

First, can you give more explanation on why the equation holds? I fail to get why the magic happens.

Second, assume it holds, does it mean the below?

I wonder if the above eq makes any sense? Because the reason we need a neural net in diffusion is we don't know the $q(\mathbf{x}_{t-1}|\mathbf{x}_t)$. Now we are saying that the forward transition and the reverse transition are the same?

I would appreciate it very much if you could give more hints on those questions. Thanks a lot!