Sampling conditioned diffusions via Pathspace Projected Monte Carlo

Tobias Grafke

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arXiv · 2506.15743

Sampling conditioned diffusions via Pathspace Projected Monte Carlo

Tobias Grafke

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Abstract

We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that adhere to the conditioning constraint. We demonstrate the effectiveness of the algorithm by sampling a dynamical condensation phase transition, conditioning a random walk on a fixed Levy stochastic area, conditioning a stochastic nonlinear wave equation on high amplitude waves, and sampling a stochastic partial differential equation model of turbulent pipe flow conditioned on relaminarization events.

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Tobias Grafke. 2025-06-17. Sampling conditioned diffusions via Pathspace Projected Monte Carlo. https://arxiv.org/abs/2506.15743

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