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Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis
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Proposes an information-theoretic generalization framework treating VAE/DM encoders and generators as randomized mappings, yielding algorithm- and data-dependent bounds and an explicit diffusion-time trade-off for score-based diffusion models.
Problem
Generalization of VAEs and diffusion models is theoretically underexplored, especially the shared encoder-generator structure and how diffusion time T affects generalization.
Approach
Model encoders and generators as randomized mappings and bound the generation-error generalization gap with sub-Gaussian losses via the mutual information I(X_hat; X | Z) plus encoder KL to the prior; for DMs this gives a T-dependent trade-off between encoder and generator generalization terms, with a computable bound from training data only.
Key results
- Theory gives a generalization bound for DMs with T1 + T2 (encoder KL terms) decreasing in T and T3 (generator mutual information) growing linearly in T, implying an explicit diffusion-time trade-off.
- On Swiss Roll, the estimated bound and test KL both show a trade-off in T with optimal T roughly in 0.4 to 0.6; on MNIST and CIFAR10 the estimated bound indicates optimal T around 0.8.
- The generator mutual information term yields sample complexity O(1/sqrt(m)), compared with O(m^{-2/5}) reported for random-feature-based analysis.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| vary diffusion time T | score-based diffusion models on Swiss Roll · Swiss Roll | test-data KL divergence: 0.4 to 0.6 | Mixed |
| vary diffusion time T | score-based diffusion models trained on few-shot data · MNIST and CIFAR10 (m=16) | estimated generalization bound: around 0.8 | Mixed |
| vary diffusion time T | score-based diffusion models trained on few-shot data · MNIST and CIFAR10 (m=16) | test-data KL divergence and log-likelihood | No clear effect |
| vary diffusion time T | score-based diffusion models trained on full data · MNIST and CIFAR10 | estimated generalization bound and test log-likelihood (BPD) | Mixed |
Surprising findings
- Longer diffusion time does not necessarily improve generalization; the test KL and BPD on real data did not clearly reflect the trade-off, unlike the estimated bound.
Limitations
- Bounds rely on sub-Gaussian loss assumption and bounded score assumption for the mutual information term.
- Real-data experiments use few-shot and tractable settings; KL and log-likelihood estimates are unreliable in high dimensions with limited data.
Experimental setup
Datasets: Swiss Roll (synthetic 2D) MNIST CIFAR10
Benchmarks: Swiss Roll (synthetic) MNIST CIFAR10
Metrics: estimated generalization bound test-data KL divergence bits per dimension (BPD) log-likelihood
Baselines: PAC-Bayes VAE generalization bound Wasserstein-based diffusion generalization bound Random feature diffusion generalization analysis
Builds on: Information-theoretic generalization bounds (Xu & Raginsky style) Score-based SDE diffusion models Variational autoencoders PAC-Bayes VAE bounds
Closest papers by meaning
- Understanding diffusion models requires rethinking (again) generalization (NeurIPS 2026 · similarity 0.90)
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- Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variables (NeurIPS 2025 · similarity 0.89)
- Unified Generation, Reconstruction, and Representation: Generalized Diffusion with Adaptive Latent Encoding-Decoding (ICML 2024 · similarity 0.89)
- Generalization Dynamics of Linear Diffusion Models (NeurIPS 2026 · similarity 0.89)
- Towards a Mechanistic Explanation of Diffusion Model Generalization (ICML 2025 · similarity 0.89)
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