Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models

This paper presents a new method that uses Neural Galerkin Normalizing Flows to efficiently approximate how probability distributions evolve in diffusion processes (mathematical models of random systems). Rather than solving complex equations from scratch each time, the method learns a reusable mathematical transformation that can quickly predict probability distributions for any starting point, while automatically ensuring the results remain valid and physically consistent. After training once, this learned model can be rapidly deployed for various practical applications like statistical inference and generating random samples.