arXiv Machine Learning
Aug 10

Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions

arXiv:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.

By Iskander Azangulov, George Deligiannidis, Judith Rousseau
arXiv Machine Learning
Jul 14

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds

arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.

By Swagatam Das, Vaclav Snasel