发表机构
Institute of Human Biology (IHB), Roche（人类生物学研究所（IHB），罗氏公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出芬斯勒流匹配（FFM）框架，从离散马尔可夫转移图学习连续随机动力学，在合成与单细胞轨迹推断基准中提升了中间种群恢复效果，保留了方向性与扩散结构。
AI 中文摘要
单细胞快照数据可解析连续的细胞状态，但无法唯一确定支配这些状态间转换的动力学。然而，额外的动力学信息通常可编码在细胞-细胞马尔可夫转移核中。现有的单细胞轨迹推断生成方法要么仅从总体边际推断迁移，要么在状态空间上施加对称几何，要么通过每个观测状态处的单个速度向量引入方向性。我们提出芬斯勒流匹配（Finsler Flow Matching, FFM），这一从离散马尔可夫转移图学习连续随机动力学的框架。我们利用一阶和二阶局部矩构建受Freidlin-Wentzell作用启发的芬斯勒结构，其中二阶矩决定各向异性可达性，一阶矩引入偏好运动方向。我们学习所得有向测地线的神经近似，利用其芬斯勒代价构建源-目标耦合，并定义几何感知随机条件路径，可通过无模拟的得分与流匹配提炼为连续生成过程。在合成数据和单细胞轨迹推断基准测试中，FFM提升了 withheld 中间种群的恢复效果，尤其在转移动力学具有强方向性或各向异性时表现突出。我们的结果为从离散转移概率到连续生成动力学提供了一条原则性路径，同时保留了方向性和扩散结构。
英文摘要
Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.
