Machine-Learned Sampling of Conditioned Path Measures

Qijia Jiang; Reuben Cohn-Gordon

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arXiv · 2506.01904

Machine-Learned Sampling of Conditioned Path Measures

Qijia Jiang·Reuben Cohn-Gordon

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Abstract

We propose algorithms for sampling from posterior path measures $P(C([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures, and (2) optimization in $\infty$-dimensional probability space endowed with a Wasserstein metric, which can be used to evolve a density curve under the specified likelihood. The resulting algorithms are theoretically grounded and can be integrated seamlessly with neural networks for learning the target trajectory ensembles, without access to data.

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Qijia Jiang, Reuben Cohn-Gordon. 2025-06-02. Machine-Learned Sampling of Conditioned Path Measures. https://arxiv.org/abs/2506.01904

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