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
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
By Ali Siahkoohi
Scaling laws promised cost-effective experiments; six years later, they have yet to fully deliver. Instead, researchers have found them unreliable at small scales (starting at 4M parameters) and concluded that sizable models cannot be avoided.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
arXiv:2605. 25811v2 Announce Type: replace-cross Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure.
By Kwangho Kim
arXiv:2607. 13491v1 Announce Type: cross Abstract: Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters.
By Shuzhen Li, Yifan Zhang, Jiacheng Guo, Quanquan Gu, Mengdi Wang
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
By Jiarui Xing, Song Wang, Jian Wang