Score matching for sub-Riemannian bridge sampling

arXiv:2404.15258v1 Announce Type: cross
Abstract: Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on Euclidean spaces, when considering diffusion processes on Riemannian manifolds the geometry brings in further complications. In even higher generality, advancing from Riemannian to sub-Riemannian geometries introduces hypoellipticity, and the possibility of finding appropriate explicit approximations for the score of the diffusion process is removed. We …

abstract arxiv bridge cs.lg data diffusion generative geometry imputation inference math.dg math.pr math.st modelling processes sampling simulation spaces statistics stat.ml stat.th stochastic tool type