Score Matching for Simulating Sub-Riemannian Diffusion Bridge Processes

Watch a 46-minute conference talk exploring advanced mathematical techniques for simulating diffusion bridge processes in sub-Riemannian geometries. Delve into the challenges of handling conditioned diffusion processes, essential for inference in stochastic processes, data imputation, and geometric statistics. Learn how recent machine learning advances can be adapted to train score approximators on sub-Riemannian manifolds, addressing the complexities introduced by hypoellipticity and non-holonomic frames. Explore the generalization of denoising loss concepts through stochastic Taylor expansion, with practical demonstrations on the Heisenberg group and adapted coordinates. Presented by Karen Habermann at the "Frontiers in Sub-Riemannian Geometry" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France, this talk represents collaborative work with Erlend Grong and Stefan Sommer.