Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces
This work addresses a gap in scalable sampling methods for infinite-dimensional spaces, with applications in simulating diffusion processes for rare events or constraints in fields like molecular dynamics.
The paper tackles the problem of sampling from Gibbs distributions in infinite-dimensional function spaces, presenting the Functional Adjoint Sampler (FAS) which achieves superior performance in transition path sampling for synthetic and real molecular systems like Alanine Dipeptide and Chignolin.
Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional 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. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.