Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
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| Format: | Preprint |
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2025
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| _version_ | 1866908480192905216 |
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| author | Lee, Justin Moradijamei, Behnaz Shakeri, Heman |
| author_facet | Lee, Justin Moradijamei, Behnaz Shakeri, Heman |
| contents | Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method's versatility. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_04351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points Lee, Justin Moradijamei, Behnaz Shakeri, Heman Machine Learning Neural and Evolutionary Computing I.2 I.2.6 Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method's versatility. |
| title | Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points |
| topic | Machine Learning Neural and Evolutionary Computing I.2 I.2.6 |
| url | https://arxiv.org/abs/2508.04351 |