从朗之万动力学视角重解扩散模型，让生成机制更直观易懂。
Rethinking the Diffusion Model from a Langevin Perspective
- 用朗之万方程统一解释扩散模型的正反过程
- 揭示ODE与SDE扩散模型的本质统一性
- 适合想深入理解原理的初学者和研究者
扩散模型常从变分自编码器（VAE）、得分匹配或流匹配等角度引入，伴随大量技术性数学推导，对初学者而言较难理解。一个核心问题是：反向过程如何从纯噪声还原数据？本文从全新的朗之万动力学视角系统梳理扩散模型，提供更简洁、清晰且直观的解答。我们进一步回答：为何基于微分方程（ODE）和随机微分方程（SDE）的扩散模型可在同一框架下统一？为何扩散模型在理论上优于普通变分自编码器？为何流匹配并不比去噪或得分匹配更基础，而是在最大似然意义下等价？我们证明，朗之万视角能清晰解答上述问题，贯通现有不同解释，展示不同形式间的可转换性，并为学习者与研究者提供深刻的直观理解与教学价值。
原文摘要 · Abstract (English)
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.
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