4 papers
Infinite-dimensional generative diffusions via Doob's h-transform
Thorben Pieper-Sethmacher, Daniel Paulin
This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising…
Guided filtering and smoothing for infinite-dimensional diffusions
Thorben Pieper-Sethmacher, Daniele Avitabile, Frank van der Meulen
We consider the filtering and smoothing problems for an infinite-dimensional diffusion process X, observed through a finite-dimensional representation at discrete points in time. A…
Simulation of infinite-dimensional diffusion bridges
Thorben Pieper-Sethmacher, Frank van der Meulen, Aad van der Vaart
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridg…
On a class of exponential changes of measure for stochastic PDEs
Thorben Pieper-Sethmacher, Frank van der Meulen, Aad van der Vaart
Given a mild solution to a semilinear stochastic partial differential equation (SPDE), we consider an exponential change of measure based on its infinitesimal generator , de…