WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911404368330752 |
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| author | Wang, Xinyu Wang, Ruoyu Peng, Qiangwei Zhou, Peijie Li, Tiejun |
| author_facet | Wang, Xinyu Wang, Ruoyu Peng, Qiangwei Zhou, Peijie Li, Tiejun |
| contents | Reconstructing dynamical evolution from limited observations is a fundamental challenge in single-cell biology, where dynamic unbalanced optimal transport provides a principled framework for modeling coupled transport and mass variation. However, existing approaches rely on trajectory simulation at inference time, making inference a key bottleneck for scalable applications. In this work, we propose a mean-flow framework for unbalanced flow matching that summarizes both transport and mass-growth dynamics over arbitrary time intervals using mean velocity and mass-growth fields, enabling fast one-step generation without trajectory simulation. To solve dynamic unbalanced optimal transport under the Wasserstein-Fisher-Rao geometry, we further build on this framework to develop Wasserstein-Fisher-Rao Mean Flow Matching (WFR-MFM). Across synthetic and real single-cell RNA sequencing datasets, WFR-MFM achieves orders-of-magnitude faster inference than a range of existing baselines while maintaining high predictive accuracy, and enables efficient perturbation response prediction on large synthetic datasets with thousands of conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20606 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport Wang, Xinyu Wang, Ruoyu Peng, Qiangwei Zhou, Peijie Li, Tiejun Machine Learning Artificial Intelligence Genomics Reconstructing dynamical evolution from limited observations is a fundamental challenge in single-cell biology, where dynamic unbalanced optimal transport provides a principled framework for modeling coupled transport and mass variation. However, existing approaches rely on trajectory simulation at inference time, making inference a key bottleneck for scalable applications. In this work, we propose a mean-flow framework for unbalanced flow matching that summarizes both transport and mass-growth dynamics over arbitrary time intervals using mean velocity and mass-growth fields, enabling fast one-step generation without trajectory simulation. To solve dynamic unbalanced optimal transport under the Wasserstein-Fisher-Rao geometry, we further build on this framework to develop Wasserstein-Fisher-Rao Mean Flow Matching (WFR-MFM). Across synthetic and real single-cell RNA sequencing datasets, WFR-MFM achieves orders-of-magnitude faster inference than a range of existing baselines while maintaining high predictive accuracy, and enables efficient perturbation response prediction on large synthetic datasets with thousands of conditions. |
| title | WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport |
| topic | Machine Learning Artificial Intelligence Genomics |
| url | https://arxiv.org/abs/2601.20606 |