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:2607. 04775v1 Announce Type: cross Abstract: Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications.
Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications. While the statistical properties of their sampling procedures are increasingly well understood, the optimization dynamics underlying their training remain less explored.
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:2609.08253v1 Announce Type: new Abstract: Diffusion models have shown remarkable performance on diverse generation tasks. Recent work finds that imposing representation alignment on the hidden...
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.
arXiv:2601. 08379v2 Announce Type: replace-cross Abstract: Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data.
arXiv:2601. 22450v2 Announce Type: replace-cross Abstract: Masked Diffusion Language Models have recently emerged as a powerful generative paradigm, yet their generalization properties remain understudied compared to their auto-regressive counterparts.
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.
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.
arXiv:2409. 02426v5 Announce Type: replace Abstract: Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood.