Path-independent Flow Matching for Multi-parameter Generative Dynamics
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arXiv
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| Format: | Preprint |
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2026
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| author | Téllez, Francisco Zamani, AmirHossein Martin, Philippe Ni, Shuang Wolf, Guy Belilovsky, Eugene Sanjari, Sina Zhang, Yanlei |
| author_facet | Téllez, Francisco Zamani, AmirHossein Martin, Philippe Ni, Shuang Wolf, Guy Belilovsky, Eugene Sanjari, Sina Zhang, Yanlei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Path-independent Flow Matching for Multi-parameter Generative Dynamics Téllez, Francisco Zamani, AmirHossein Martin, Philippe Ni, Shuang Wolf, Guy Belilovsky, Eugene Sanjari, Sina Zhang, Yanlei Machine Learning 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. |
| title | Path-independent Flow Matching for Multi-parameter Generative Dynamics |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.13487 |