The paper investigates why diffusion models, despite their practical success, can fully memorize training data when optimal. It shows that as training proceeds, the denoising objective causes overfitting at intermediate noise levels, creating a gap between validation and training performance. In a 2D toy model, this gap arises from the interplay between model error and the data distribution’s support density, leading to a smooth, generalizing flow field rather than exact recall of training points. The study also reveals that predictions from intermediate inference states become increasingly similar to training data in feature space, even as overall similarity to validation data remains unchanged.
arXiv:2310. 05264v5 Announce Type: replace Abstract: In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often yield remarkably similar outputs.
arXiv:2609.37974v1 Announce Type: cross Abstract: Masked diffusion models (MDMs) generate text by unmasking several tokens per step, but they are trained and sampled under different conditions. The m...
The paper demonstrates that diffusion models encode memorization in the geometry of their learned energy landscape before it becomes visible in generated samples. By analyzing score divergence and basin volume, the authors show that localized basins form around training images early in training, and that cyclic denoising can recover these images even when one‑shot generation shows no copies. Experiments on Gaussian mixtures, CelebA, CIFAR‑10, and Stable Diffusion v1.4 confirm that basin geometry reveals memorization across various settings.
arXiv:2512. 20963v3 Announce Type: replace Abstract: Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective.
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
arXiv:2606. 09718v1 Announce Type: new Abstract: Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored.
arXiv:2607. 02671v1 Announce Type: cross Abstract: Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good generalization but can actively benefit it.
The paper argues that the concrete random noise used in diffusion models is not merely a passive perturbation but a learnable input that can be exploited by the model. By analyzing how clean data and realized noise jointly form the noisy input, the authors show that the model can learn regularities in the data or in the noise structure, and that these two routes can interact. Experiments on MNIST and CIFAR‑10 using pseudorandom streams demonstrate that structured‑noise training can reduce prediction loss, but this advantage disappears when test noise is replaced with IID noise, indicating that the learned dependence is tied to the specific noise structure.
arXiv:2609.39648v1 Announce Type: cross Abstract: Diffusion models are typically viewed as stochastic processes that transform noise into data. We take a complementary perspective: a diffusion model...
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery. To address this, we introduce analytically tractable Bayesian information restricted diffusion (BIRD) models, in which each pixel observes restricted information about noisy data.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.