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

TL;DR

This paper introduces a unified information-theoretic framework to analyze and guarantee the generalization of VAEs and Diffusion Models, addressing theoretical gaps and providing practical bounds for model selection.

Contribution

It offers the first comprehensive theoretical analysis of generalization in VAEs and DMs, incorporating shared encoder-generator structures and enabling data-driven model optimization.

Findings

Provides explicit generalization bounds for VAEs and DMs.

Identifies a trade-off in diffusion time T affecting generalization.

Empirical validation on synthetic and real datasets supports the theory.

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.