Rethinking the Diffusion Model from a Langevin Perspective
For researchers and learners in generative modeling, this work offers a conceptual unification and intuitive explanation of diffusion models, but it is primarily pedagogical and does not introduce new algorithms or empirical results.
The paper reinterprets diffusion models from a Langevin perspective, providing a simpler and more intuitive explanation of the reverse process and unifying ODE-based and SDE-based formulations. It demonstrates that this perspective clarifies theoretical relationships, such as the equivalence of flow matching and score matching under maximum likelihood, offering pedagogical value for understanding diffusion models.
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.