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Machine-Learned Sampling of Conditioned Path Measures

arXiv 2506.01904 ↗First posted 2 Jun 2025stat.ML cs.LG stat.COcited by 0

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Abstract (arXiv)

We propose algorithms for sampling from posterior path measures P(C([0, T], ℝd)) under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures, and (2) optimization in ∞-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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 35 references that are in the map. First posted on arXiv 2 Jun 2025.

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References · 19

  1. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  2. 2016Input Convex Neural Networkscited by 414
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  7. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
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  11. 2022Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Pathscited by 38
  12. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 30
7 more
  1. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 27
  2. 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
  3. 2024Stein transport for Bayesian inferencecited by 11
  4. 2015A variational approach to path estimation and parameter inference of hidden diffusion processescited by 10
  5. 2018An entropy minimization approach to second-order variational mean-field gamescited by 9
  6. 2023Diffusion Methods for Generating Transition Pathscited by 8
  7. 2024A variational approach to sampling in diffusion processescited by 4

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