I'm trying to understand the Sohl-Dickstein 2015 paper (https://arxiv.org/pdf/1503.03585.pdf) on generative diffusion probabilistic models, and for the longest time was hung up on how the reverse process could work. Clearly, a reverse random walk is very unlikely to go back to the original spot. Then I realized that we just need to "fine-tune" the mean and stdev to make it go backwards. Here is a simple example that brute forces that: https://colab.research.google.com/drive/151u9xjBIF-bxbASym9tbvlcWWT83rMjq?usp=sharing