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VAE 与扩散模型的泛化能力：统一的信息论分析框架

Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis

Authors: Qi Chen, Jierui Zhu, Florian Shkurti
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Identifiers: arXiv:2506.00849 [cs.LG] | DOI: 10.48550/arXiv.2506.00849
Status: ICLR 2025 Accepted

文章背景与核心概要

变分自编码器 (Variational Autoencoder, VAE) 与扩散模型 (Diffusion Model, DM) 在现代图像生成与多模态表征中取得了巨大成功，但两者在理论层面的泛化表现——尤其是基于共享的“编码器-生成器”架构下的泛化机理，长期以来缺乏统一且深入的数学刻画。本文提出了一套建立在现代信息论工具之上的统一分析框架，通过将编码器与生成器均视为随机映射，为生成模型的泛化性能提供了严格的理论保证。该框架不仅弥补了过去 VAE 理论分析中忽略生成器泛化能力的缺陷，还明确推导出了扩散模型泛化界与扩散时间步 \(T\) 之间的平衡权衡，并提供了完全由训练数据驱动的可计算理论界，可直接融入训练损失以进一步提升生成质量。该工作已被 ICLR 2025 接收。

📌 内容概要

📌 Summary

尽管扩散模型 (Diffusion Models, DMs) 与变分自编码器 (Variational Autoencoders, VAEs) 在实际应用中取得了惊人的实证成功，但它们的理论泛化性能仍未得到深入探究，尤其是对于它们共有的“编码器-生成器”架构在泛化机制上的分析严重不足。

Despite the immense empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their theoretical generalization performance has remained largely underexplored—particularly concerning their shared encoder-generator architectures.

本文提出了一个统一的信息论分析框架，将编码器与生成器均建模为随机映射 (Randomized Mappings) ，为两者的泛化表现提供了严格的理论保证。

This paper introduces a unified information-theoretic framework that treats both encoders and generators as randomized mappings to provide rigorous generalization guarantees.

核心贡献：

Key Contributions:

  1. 更精细的 VAE 分析：通过全面考量生成器的作用 (以往工作中常被忽视) ，对 VAE 的泛化表现给出了更为系统完备的评估。
  2. 扩散模型的泛化权衡：清晰揭示了扩散模型在泛化层面的显式权衡关系，证明该权衡高度依赖于扩散时间步 \(T\)。
  3. 数据驱动的可计算界：为扩散模型推导出仅依据训练数据即可计算的理论泛化界，不仅能用于指导选取最优扩散时间 \(T\)，还能直接融入模型优化目标以提升生成性能。
  1. Refined VAE Analysis: Offers a more comprehensive evaluation of VAE generalization by properly accounting for the generator's role, an aspect often overlooked in prior work.
  2. Diffusion Model Trade-Offs: Illustrates an explicit generalization trade-off for DMs that depends heavily on the diffusion time \(T\).
  3. Computable Bounds: Provides data-driven computable bounds for DMs, enabling both the selection of the optimal diffusion time \(T\) and the integration of these bounds directly into the model optimization process to enhance performance.

在合成数据集与真实世界数据集上的实证评估，均验证了本文所提理论框架的有效性。

Empirical validations on both synthetic and real-world datasets confirm the effectiveness of the proposed theoretical framework.

📄 论文摘要

📄 Abstract

尽管扩散模型 (DMs) 与变分自编码器 (VAEs) 取得了实证上的巨大成功，但它们的泛化性能在理论上仍未得到充分探索，尤其是缺乏对共享编码器-生成器结构的全面审视。借助最新的信息论工具，我们提出了一套统一的理论框架，将编码器与生成器均视为随机映射，从而为两者的泛化表现提供了理论保障。该框架进一步实现了：(1) 对 VAE 开展精细化分析，补全了以往被忽视的生成器泛化问题；(2) 阐明了扩散模型中与扩散时间 \(T\) 紧密相关的显式泛化权衡；(3) 仅依托训练数据为扩散模型提供了可计算界，不仅支持最优时间步 \(T\) 的选取，还允许将此类界直接整合到优化流程中以改善模型表现。在合成数据集和真实数据集上的实验结果均印证了本理论的正确性。

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator structure. Leveraging recent information-theoretic tools, we propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator by treating them as randomized mappings. This framework further enables (1) a refined analysis for VAEs, accounting for the generator's generalization, which was previously overlooked; (2) illustrating an explicit trade-off in generalization terms for DMs that depends on the diffusion time \(T\); and (3) providing computable bounds for DMs based solely on the training data, allowing the selection of the optimal \(T\) and the integration of such bounds into the optimization process to improve model performance. Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.

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🕒 Submission History

  • [v1] 2025年6月1日 06:11:38 UTC (942 KB)
  • [v2] 2026年9月9日 20:06:32 UTC (937 KB) — 当前版本
  • [v1] Sun, 1 Jun 2025 06:11:38 UTC (942 KB)
  • [v2] Wed, 9 Sep 2026 20:06:32 UTC (937 KB) — Current Version