Diffusion Models for Arbitrary Discrete Markov Processes

Applied and Computational Mathematics Seminar
Monday, March 4, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005 and https://gatech.zoom.us/j/98355006347
Zachary Fox – Oak Ridge National Laboratory – zachrfox@gmail.comhttps://zachfox.github.io/
Molei Tao

Please Note: Speaker will present in person.

Diffusion models have become ubiquitous for image generation and are increasingly being used for scientific applications. To date, many flavors of diffusion models have been developed by varying the stochastic process that noises data, but also the domain on which these processes act. Typically, generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact analysis. We relate the theory to the existing continuous-state Gaussian diffusion in discrete and continuous time. This approach is validated using a simple stochastic decay process, in which the reverse process generates images from a single all-black image, rather than a noisy prior distribution.