When calculating the exact likelihood, why you do not add uniform noise to the input image?

[huanranchen]

Hi~
According to the definition of bpd

We should calculate the likelihood of x+u to approximate the bpd.

However, in this code, it directly calculate the likelihood of x instead of x+u. I test some image, and it even give me negative bpd (which means the probability of generating such image is greater than 1). Is this wrong?

[daihuiao]

Hello, I am also learning the likelihood calculation in score sde. Although I did not understand the formula you attached above, I feel that there is something wrong with the code implementation in the project.

I noticed that in the original code, the prior log probability (prior_logp) is calculated using this line. This formula calculates prior_logp based on the final output of the ODE solver (see line 101: zp = solution.y[:, -1]), which means the prior log probability is computed by inputting the final denoised image into a Gaussian distribution.

However, according to the formula in the paper, the final likelihood should be the likelihood of the Gaussian distribution plus an integral term. Am I misunderstanding something?

Any response would be greatly appreciated.