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

• URL: http://arxiv.org/abs/2506.00849v1
• Date: Sun, 01 Jun 2025 06:11:38 GMT
• Title: Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis
• Authors: Qi Chen, Jierui Zhu, Florian Shkurti,
• Abstract summary: We propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator.<n> Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.
• Score: 20.429383584319815
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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