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arXiv · 2605.13487

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Francisco Téllez·AmirHossein Zamani·Philippe Martin·Shuang Ni·Guy Wolf·Eugene Belilovsky·Sina Sanjari·Yanlei Zhang
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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.

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Francisco Téllez, AmirHossein Zamani, Philippe Martin, Shuang Ni, Guy Wolf, Eugene Belilovsky, Sina Sanjari, Yanlei Zhang. 2026-05-13. Path-independent Flow Matching for Multi-parameter Generative Dynamics. https://arxiv.org/abs/2605.13487

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