arXiv Machine Learning
Sep 24

Localized Diffusion Models

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 Machine Learning
Sep 21

Sparse Priors for Efficient Distribution Learning

arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.

By Saumya Goyal, Barnab\'as P\'oczos