Infinite Dimensional Adjoint Sampler: Scalable Sampling on Function Spaces

We present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control (SOC)-based diffusion sampler that operates directly in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Function space Adjoint Sampler (FAS) generalizes adjoint sampling Havens et al. (2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. Through experiments, we show its effectiveness on transition-path sampling.