mlsanityData to 7 Oct 2026

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

arXiv 2506.00849 ↗First posted 1 Jun 2025cs.LG cs.AIcited by 2

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 67 of its 94 references that are in the map. First posted on arXiv 1 Jun 2025.

Builds on

67 of 94 references.

Closest ancestors · 18

Same direction, newest first

  1. 2023On the Generalization Properties of Diffusion Models3 Nov
  2. 2022Scalable Diffusion Models with Transformers19 Dec
  3. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  4. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  6. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  7. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  8. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models10 Jun
  9. 2022Score-Based Generative Models Detect Manifolds2 Jun
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Variational Diffusion Models1 Jul
  12. 2021Score-based Generative Modeling in Latent Space10 Jun
6 more
  1. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  2. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Implicit Models6 Oct
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 49

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2019An Introduction to Variational Autoencoderscited by 997
  5. 2016Conditional Image Generation with PixelCNN Decoderscited by 859
  6. 2022Quantifying Memorization Across Neural Language Modelscited by 755
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  9. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  10. 2017Wasserstein Auto-Encoderscited by 371
  11. 2015Adversarial Autoencoderscited by 359
  12. 2017Information-theoretic analysis of generalization capability of learning algorithmscited by 299
37 more
  1. 2015A note on the evaluation of generative modelscited by 291
  2. 2023An Edit Friendly DDPM Noise Space: Inversion and Manipulationscited by 243
  3. 2021User-friendly introduction to PAC-Bayes boundscited by 234
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  5. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  6. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
  7. 2020Reasoning About Generalization via Conditional Mutual Informationcited by 145
  8. 2019Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimatescited by 118
  9. 2019Tightening Mutual Information Based Bounds on Generalization Errorcited by 117
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  11. 2023Improving Tuning-Free Real Image Editing with Proximal Guidancecited by 87
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  15. 2020Simple and Effective VAE Training with Calibrated Decoderscited by 57
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  20. 2020Some Theoretical Insights into Wasserstein GANscited by 28
  21. 2022A New Family of Generalization Bounds Using Samplewise Evaluated CMIcited by 28
  22. 2022The dynamics of representation learning in shallow, non-linear autoencoderscited by 27
  23. 2022Fair Representation Learning through Implicit Path Alignmentcited by 22
  24. 2023Tighter Information-Theoretic Generalization Bounds from Supersamplescited by 21
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  29. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16
  30. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  31. 2021VAE Approximation Error: ELBO and Exponential Familiescited by 12
  32. 2023Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealingcited by 12
  33. 2020Generalization and Memorization: The Bias Potential Modelcited by 9
  34. 2022Variational Laplace Autoencoderscited by 7
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  36. 2024Intersectional Unfairness Discoverycited by 5
  37. 2019Adversarial Networks and Autoencoders: The Primal-Dual Relationship and Generalization Boundscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Modelscited by 4
  2. 2026Proof-of-Authorship for Diffusion-based AI Generated Contentcited by 0

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