Could you explain the q_sample ?

[sandeepjangir07]

The return of the q_sample function is defined as : return (continuous_sqrt_alpha_cumprod * x_start + (1 - continuous_sqrt_alpha_cumprod**2).sqrt() * noise)

I do not understand this part . (1 - continuous_sqrt_alpha_cumprod**2).sqrt() : Why there is a need for square and the square root afterwards. I could not find anything in the main paper or the following paper that SR3 using to define their noise schedule. Some explanation would be good to understand it.

Thank you.

[kada0720]

@sandeepjangir07 I have the same question

[include5636]

@kada0720 @sandeepjangir07

You can find it in DDPM page 4

Here continuous_sqrt_alpha_cumprod is $\sqrt{\bar{\alpha}_t}$, thus continuous_sqrt_alpha_cumprod**2 equals to $\bar{\alpha}_t$

Besides, you could find similar formula in SR3 paper on the top left corner of page 3.