Rethinking the Diffusion Model from a Langevin Perspective

TL;DR

This paper presents a unified Langevin perspective on diffusion models, simplifying their understanding, connecting various formulations, and addressing fundamental questions about their theoretical advantages.

Contribution

It offers a new, intuitive Langevin-based framework that unifies different diffusion model formulations and clarifies their theoretical strengths.

Findings

Unifies ODE and SDE diffusion models under a single framework.

Provides clearer explanations of how reverse processes generate data.

Demonstrates the theoretical superiority of diffusion models over VAEs.

Abstract

Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question is: how does the reverse process invert the forward process to generate data from pure noise? This article systematically organizes the diffusion model from a fresh Langevin perspective, offering a simpler, clearer, and more intuitive answer. We also address the following questions: how can ODE-based and SDE-based diffusion models be unified under a single framework? Why are diffusion models theoretically superior to ordinary VAEs? Why is flow matching not fundamentally simpler than denoising or score matching, but equivalent under maximum-likelihood? We demonstrate that the Langevin perspective offers clear and straightforward answers to these questions, bridging existing interpretations of diffusion models, showing how different formulations can be converted into one another within a common framework, and offering pedagogical value for both learners and experienced researchers seeking deeper intuition.