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

2025-08-06

AI Summary

Modeling high-dimensional dynamical systems from sparse, irregularly timed snapshots remains challenging, especially when dimensionality reduction is undesirable. Method: We propose Multi-marginal Stochastic Flow Matching (MSFM), a framework that directly learns continuous probabilistic evolution paths in the original high-dimensional space—without dimensionality reduction. MSFM generalizes simulation-free score matching and flow matching to the multi-marginal setting and incorporates measure-valued splines to explicitly model irregular temporal sampling. Contribution/Results: By jointly optimizing multi-time marginal distribution constraints and flow consistency, MSFM yields robust, differentiable, and generalizable probability path estimates. Experiments on single-cell gene expression time-series and image evolution tasks demonstrate its ability to accurately recover dynamic structures under non-uniform sampling, while exhibiting strong resistance to overfitting.

Technology Category

• Machine Learning: Multimodal Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Modeling high-dimensional systems from irregular snapshots
• Avoiding oversimplification of dynamics in non-equilibrium systems
• Aligning high-dimensional data without dimensionality reduction

Innovation

• Multi-Marginal Stochastic Flow Matching for alignment
• Measure-valued splines enhance timing robustness
• Score matching prevents high-dimensional overfitting