Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points

TL;DR

This paper introduces MMSFM, a novel method for modeling high-dimensional system evolution from irregular snapshot data without dimensionality reduction, using measure-valued splines and score matching for robustness and accuracy.

Contribution

We develop Multi-Marginal Stochastic Flow Matching, extending score and flow matching to handle multiple non-equidistant data snapshots in high dimensions without dimensionality reduction.

Findings

Successfully applied to synthetic datasets showing accurate dynamics reconstruction.

Effective on gene expression data with irregular sampling.

Versatile in image progression tasks.

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, including gene expression data collected at uneven time points and an image progression task, demonstrating the method's versatility.