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

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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2506.00849 [cs.LG]

(or arXiv:2506.00849v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2506.00849 Focus to learn more arXiv-issued DOI via DataCite

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