将扩散模型重新理解为变分自编码器的扩展，揭示其核心优化目标。
Schödinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders
- 用数据处理不等式重构薛定谔桥模型，将其视为变分自编码器的延伸。
- 目标函数由先验损失和漂移匹配两部分构成，理论更清晰。
- 适合研究扩散模型原理或想理解其与自编码器关系的读者。
生成式扩散模型通过前向和反向随机微分方程连接数据分布与先验分布。传统扩散模型（如基于得分的模型）仅学习反向过程，而更灵活的框架通过引入薛定谔桥（SB）也学习前向过程。然而，由于SB模型背后的数学结构复杂，其目标函数难以直观理解。本文提出统一框架，将SB型模型重新解释为变分自编码器的扩展。在此视角下，数据处理不等式起关键作用，发现目标函数由先验损失和漂移匹配两部分组成。
原文摘要 · Abstract (English)
Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more flexible frameworks have been proposed to also learn the forward process by employing the Schrödinger bridge (SB). However, due to the complexity of the mathematical structure behind SB-type models, we can not easily give an intuitive understanding of their objective function. In this work, we propose a unified framework to construct diffusion models by reinterpreting the SB-type models as an extension of variational autoencoders. In this context, the data processing inequality plays a crucial role. As a result, we find that the objective function consists of the prior loss and drift matching parts.
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