Designing Generative Models from General Markov Processes: Framework and Application

Data Science Seminar

Yinuo Ren
Stanford

Abstract

Dynamical systems and stochastic processes provide a foundation for generative modeling, with Brownian motion and jump processes serving as key ingredients in diffusion models. In this talk, I present a unified framework for designing generative models from general Markov processes. Under suitable assumptions, the framework provides constructions of time-reversed dynamics and trainable objectives that control the discrepancy between data and generated distributions. It recovers continuous and discrete diffusion models within a common formulation and supports new designs tailored to different modeling problems.

As an application, I introduce multi-mask diffusion language models. In standard masked diffusion, complete corruption produces a single all-mask state, a zero-entropy starting point that complicates consistency-based generation. To address this, we introduce multiple mask states that provide a random starting point, derive a training objective within the framework, and apply consistency distillation for few-step generation. Controlled experiments on unconditional text generation show lower generative perplexity at matched token entropy and competitive few-step performance after distillation."