Diffusion Processes on Implicit Manifolds

ArXi:2604.07213v1 Announce Type: new High-dimensional data are often modeled as lying near a low-dimensional manifold. We study how to construct diffusion processes on this data manifold in the implicit setting. That is, using only point cloud samples and without access to charts, projections, or other geometric primitives. Our main contribution is a data-driven SDE that captures intrinsic diffusion on the underlying manifold while being defined in ambient space.