The paper introduces localized diffusion models, which exploit locality structure—sparse conditional dependencies among target variables—to reduce the dimensionality of the score function. By training a localized neural network with a localized score matching loss, the authors demonstrate that diffusion models can achieve dimension‑independent error bounds, balancing statistical and localization errors with a moderate radius. This approach also enables parallel training, potentially improving efficiency for large‑scale applications.
By Georg A. Gottwald, Shuigen Liu, Youssef Marzouk, Sebastian Reich, Xin T. Tong
arXiv:2608.23696v1 Announce Type: new
Abstract: Despite their remarkable success in modeling complex data, generative models face a fundamental tradeoff. Global approaches can capture full structural...
By Kanta Masuki, Yuto Ashida
arXiv:2607. 17099v1 Announce Type: cross Abstract: Recent geometric foundation models (e.
By Feng Xue, Wu Chen, Mingshuai Zhao, Guofeng Zhong, Anlong Ming, Haozhe Wang, Dianqiao Lei, Zhaowen Lin, Haiyang Zhang, Nicu Sebe
arXiv:2605.12597v3 Announce Type: replace-cross
Abstract: Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently ena...
By Luca Maria Del Bono, Giulio Biroli, Patrick Charbonneau, Marylou Gabri\'e
arXiv:2608. 11859v1 Announce Type: new Abstract: Scaling laws promised cost-effective experiments; six years later, they have yet to fully deliver.
By Nicholas Lourie, Kyunghyun Cho, Karen Ullrich, Sanae Lotfi
arXiv:2607. 29053v1 Announce Type: new Abstract: Standard model comparison is global, aggregating losses across the covariate space to declare a single winner.
By Yi Zhou, Baishi Li, Xuan Yao, Ke-Wei Huang