无需降维，直接建模不同时点的高维数据演化过程
Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
- 用多边缘随机流匹配方法对非等距时间点数据建模
- 在基因表达和图像演化任务中准确还原动态轨迹
- 适合生物、医学等领域高维不规则观测数据研究
从有限且不规则时间点的高维快照观测中建模系统演化，在定量生物学等领域面临重大挑战。传统方法常依赖降维，易简化动态并忽略非平衡系统中的关键瞬态行为。本文提出多边缘随机流匹配（MMSFM），将无仿真评分与流匹配方法扩展至多边缘设置，可在不降维情况下对非等距时间点的高维数据进行对齐。通过测度值样条增强对不规则采样时间的鲁棒性，评分匹配防止高维空间过拟合。我们在多个合成与基准数据集上验证框架，包括不等时点采集的基因表达数据和图像演化任务，证明方法具有强泛化能力与适用性。
原文摘要 · Abstract (English)
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.
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