# Machine-Learned Sampling of Conditioned Path Measures

arXiv: https://arxiv.org/abs/2506.01904 · HTML: https://mlsanity.com/paper/2506.01904/

## 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.

## Builds on (most cited first, 19 of 19)

- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modeling](https://mlsanity.com/paper/2304.00917/) (2023)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [Conditioning Diffusions Using Malliavin Calculus](https://mlsanity.com/paper/2504.03461/) (2025)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [A variational approach to path estimation and parameter inference of hidden diffusion processes](https://mlsanity.com/paper/1508.00506/) (2015)
- [An entropy minimization approach to second-order variational mean-field games](https://mlsanity.com/paper/1807.09078/) (2018)
- [Diffusion Methods for Generating Transition Paths](https://mlsanity.com/paper/2309.10276/) (2023)
- [A variational approach to sampling in diffusion processes](https://mlsanity.com/paper/2405.00126/) (2024)

## 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.