Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis
This work addresses a theoretical gap for researchers in generative modeling, offering insights into generalization trade-offs, though it is incremental as it builds on existing models without introducing new paradigms.
The paper tackles the lack of theoretical understanding of generalization in VAE and diffusion models by proposing a unified information-theoretic framework that provides generalization guarantees for both encoder and generator components, with empirical validation on synthetic and real datasets.
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.