Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
This addresses a challenge in quantitative biology for modeling non-equilibrium systems from limited irregular observations, though it appears incremental as an extension of flow matching methods.
The paper tackles modeling high-dimensional system evolution from irregular snapshot observations by introducing Multi-Marginal Stochastic Flow Matching (MMSFM), which aligns high-dimensional data at non-equidistant time points without dimensionality reduction and demonstrates versatility on synthetic and benchmark datasets including gene expression and image progression tasks.
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.