Abstract:Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.
| Comments: | 12 pages including references for main part of the document, 26 pages in total when including the appendix. 15 figures in total |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13487 [cs.LG] |
| (or arXiv:2605.13487v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13487 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Francisco Téllez [view email]
[v1]
Wed, 13 May 2026 13:12:50 UTC (28,100 KB)