Multi-Marginal Stochastic Flow Matching for Alignment of High-Dimensional Snapshot Data at Irregular Time Points
Keywords: Multi-marginal Snapshot data flow matching, Measure-valued spline interpolation, Single-cell data, Optimal Transport
TL;DR: A flow matchings method that aligns multiple high-dimensional snapshot data collected at arbitrary time points.
Abstract: 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 and apply it to single-cell perturbation data from melanoma cell lines and gene expression data collected at uneven time points.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 13058
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