On the Mathematics of Diffusion Models

This paper presents the stochastic differential equations of diffusion models assuming only familiarity with Gaussian distributions. This treatment of the diffusion model SDE and the associated reverse-time SDEs unifies the VAE and score-matching treatments. It also yields the contribution of this paper -- a novel likelihood formula derived from a non-variational VAE analysis (equations (10) and (12) in the text). The paper presents the mathematics directly with attributions saved for a final section.