Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
Justin Lee, Behnaz Moradijamei, Heman Shakeri
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.
BibTeX
@inproceedings{
lee2025multimarginal,
title={Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points},
author={Justin Lee and Behnaz Moradijamei and Heman Shakeri},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=ZLyb8DwXXE}
}