I am trying to understand Diffusion Probabilistic Models, in particular the paper by (Sohl-Dickstein et al. 2015 https://arxiv.org/abs/1503.03585). When defining the backward diffusion model, they take the conditional probability of one step de-noising to be normally distributed:
They argue that this can be done because the reversal of the diffusion process has the identical functional form as the forward diffusion. What do they mean by this? Does someone have a good reference where this is explained in more detail? Many thanks for your help!
I tried looking at the reference given in the paper:
Feller, W. On the theory of stochastic processes, with par- ticular reference to applications. In Proceedings of the [First] Berkeley Symposium on Mathematical Statistics and Probability. The Regents of the University of Cali- fornia, 1949.
However, I am struggling to find a satisfactory answer within that particular reference.
