Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces

2025-11-09

AI Summary

This work addresses the challenge of efficient sampling from Gibbs distributions in infinite-dimensional function spaces, particularly for rare-event simulation and diffusion path sampling under boundary constraints. We propose the Functional Adjoint Sampler (FAS), the first adjoint sampling framework extended to Hilbert spaces. Grounded in stochastic optimal control theory and the stochastic maximum principle, FAS constructs a scalable functional matching objective, enabling direct gradient-based optimization and sampling of conditional diffusion processes in continuous path space. Integrating variational inference with function-space diffusion modeling, FAS operates natively in infinite dimensions—without finite-dimensional approximations. We validate FAS on synthetic potential landscapes and real molecular systems (alanine dipeptide and chignolin), demonstrating substantial improvements in both efficiency and accuracy of transition-path sampling. This work establishes a new paradigm for infinite-dimensional Bayesian inversion and nonequilibrium path sampling.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

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.

Problem

• Sampling Gibbs distributions in infinite-dimensional function spaces
• Simulating diffusion process trajectories with rare event constraints
• Developing scalable functional sampling for molecular system applications

Innovation

• Adjoint sampler for infinite-dimensional function spaces
• Stochastic optimal control-based diffusion sampler
• Scalable matching objective for functional representation