从VAE到DDPM，手把手推导扩散模型核心原理
Diffusion Model from Scratch
- 用数学推导串联变分自编码器到扩散模型的发展脉络
- 揭示去噪过程与概率建模的内在联系，厘清关键步骤
- 适合想深入理解生成模型底层机制的初学者
扩散生成模型目前是主流的生成模型。然而其建模过程较为复杂，直接从开创性论文《去噪扩散概率模型》（DDPM）入手学习颇具挑战。本文旨在通过详尽的数学推导与问题导向的分析方法，帮助读者追溯从变分自编码器（VAEs）到DDPM的演进路径，建立对生成模型的基础认知。同时，探讨当前主流方法的核心思想与改进策略，为对扩散模型感兴趣的本科生和研究生提供学习指引。
原文摘要 · Abstract (English)
Diffusion generative models are currently the most popular generative models. However, their underlying modeling process is quite complex, and starting directly with the seminal paper Denoising Diffusion Probability Model (DDPM) can be challenging. This paper aims to assist readers in building a foundational understanding of generative models by tracing the evolution from VAEs to DDPM through detailed mathematical derivations and a problem-oriented analytical approach. It also explores the core ideas and improvement strategies of current mainstream methodologies, providing guidance for undergraduate and graduate students interested in learning about diffusion models.
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