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arXiv · 2506.00849

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

Qi Chen·Jierui Zhu·Florian Shkurti
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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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Qi Chen, Jierui Zhu, Florian Shkurti. 2025-06-01. Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis. https://arxiv.org/abs/2506.00849

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