ICML 2025

Multi-Marginal Stochastic Flow Matching
for High-Dimensional Snapshot Data at Irregular Time Points
Justin Lee 1 Behnaz Moradijamei 2 Heman Shakeri 1
Abstract
Modeling the evolution of high-dimensional sys-
tems from limited snapshot observations at irreg-
ular time points poses a significant challenge in
quantitative biology and related fields. Traditional
approaches often rely on dimensionality reduction
techniques, which can oversimplify the dynam-
ics 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 val-
idate our framework on several synthetic and
benchmark datasets, including gene expression
data collected at uneven time points and an im-
age progression task, demonstrating the method’s
versatility.1
1. Introduction
Understanding cellular responses to perturbations is a fun-
damental challenge in quantitative biology, with significant
implications for fields such as developmental biology, can-
cer research, and drug discovery (Altschuler & Wu, 2010;
Saeys et al., 2016). Modeling these responses requires cap-
turing complex stochastic dynamics in high-dimensional
cellular states that evolve over time under the influence of
1School of Data Science, University of Virginia, Charlottesville
VA, USA. 2James Madison University, Harrisonburg VA, USA.
Correspondence to: Justin Lee <jgh2xh@virginia.edu>, Heman
Shakeri <hs9hd@virginia.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(s).
1Code
available
at
https://github.com...