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.
By Stanislas Strasman (SU, LPSM), Sobihan Surendran (SU, LPSM), Sylvain Le Corff (SU, LPSM)
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.
By Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian, John Sous, Theodor Misiakiewicz
arXiv:2607. 23226v1 Announce Type: new Abstract: Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped.
By Jinshu Huang, Yiming Jiang, Chunlin Wu
arXiv:2502. 04646v2 Announce Type: replace-cross Abstract: Weighted sampling -- sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function -- is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more.
By Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo de Veciana
arXiv:2501. 12982v3 Announce Type: replace-cross Abstract: This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling.
By Jiadong Liang, Zhihan Huang, Yuxin Chen
arXiv:2606. 16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration.
By M. Berk Sahin, Ahmet Ege Tanriverdi, Behzad Sharif, Abolfazl Hashemi