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

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.

@article{chen2025_2506.00849,
  title={ Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis },
  author={ Qi Chen and Jierui Zhu and Florian Shkurti },
  journal={arXiv preprint arXiv:2506.00849},
  year={ 2025 }
}