How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework

Understand

Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference.

• However, the error analysis for discrete diffusion models remains less well-understood.
• In this work, we propose a comprehensive framework for the error analysis of discrete diffusion models based on L\'evy-type stochastic integrals.
• By generalizing the Poisson random measure to that with a time-independent and state-dependent intensity, we rigorously establish a stochastic integral formulation of discrete diffusion models and provide the corresponding change of measure theorems that are intriguingly analogous to It\^o integrals and Girsanov's theorem for their continuous counterparts.