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This paper re-examines diffusion models through the lens of Langevin dynamics, providing a more intuitive and unified understanding of their underlying mechanisms. It clarifies the reverse diffusion process as an approximation of Langevin dynamics and demonstrates how ODE-based and SDE-based diffusion models can be unified. The paper further elucidates the theoretical advantages of diffusion models over VAEs and the equivalence of flow matching to denoising score matching under maximum likelihood estimation.
Diffusion models, often shrouded in mathematical complexity, become surprisingly intuitive when viewed through the lens of Langevin dynamics, revealing connections between seemingly disparate formulations.
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.