Wrong Likelihood Computation for VE SDE

[lujiazho]

score_sde_pytorch/sde_lib.py

Line 244 in cb1f359

return -N / 2. * np.log(2 * np.pi * self.sigma_max ** 2) - torch.sum(z ** 2, dim=(1, 2, 3)) / (2 * self.sigma_max ** 2)

I think this line should be

-N / 2. * np.log(2 * np.pi * self.sigma_max ** 2) - torch.sum((z-x) ** 2, dim=(1, 2, 3)) / (2 * self.sigma_max ** 2)

where the x is the initial x0 which should be passed into this function

instead of

-N / 2. * np.log(2 * np.pi * self.sigma_max ** 2) - torch.sum(z ** 2, dim=(1, 2, 3)) / (2 * self.sigma_max ** 2)

isn't it?

[daihuiao]

As I understand it, the prior probabilities are calculated here, and the final distribution is assumed to be a Gaussian distribution with a mean of 0, so x in (z-x) =0。
In addition, there is no x in the function parameter pass
：）

[lujiazho]

As I understand it, the prior probabilities are calculated here, and the final distribution is assumed to be a Gaussian distribution with a mean of 0, so x in (z-x) =0。 In addition, there is no x in the function parameter pass ：）

Thanks for your reply :) To my understanding, the prior is the p(x_T) which for VE SDE is as below

where the mean is actually x0 not 0