Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make path-space laws non-identifiable from finitely many marginals, leaving held-out marginal prediction as the dominant but limited evaluation protocol. We introduce a general framework for estimating the Kullback-Leibler divergence (KL) divergence between probability measures on function space, yielding a tractable, data-driven estimator that is scalable to realistic snapshot datasets. We validate the accuracy of our estimator on a benchmark suite, where the estimated functional KL closely matches the analytic KL. Applying this framework to synthetic and real scRNA-seq datasets, we show that current evaluation metrics often give inconsistent assessments, whereas path-space KL enables a coherent comparison of trajectory inference methods and exposes discrepancies in inferred dynamics, especially in regions with sparse or missing data. These results support functional KL as a principled criterion for evaluating trajectory inference under partial observability.

翻译：轨迹推断旨在从快照数据中恢复潜在动态过程，此类数据仅能观测到时间索引边际分布的独立样本。在单细胞基因组学等应用中，破坏性测量使得路径空间法则无法通过有限个边际分布实现可辨识性，导致留出边际预测成为主导但存在局限性的评估协议。我们提出一个通用框架，用于估计函数空间上概率测度间的库尔贝克-莱布勒散度，进而得到可处理且适用于实际快照数据集的统计驱动估计量。通过基准测试套件验证，本估计量的函数KL散度估计值与解析KL散度高度吻合。将该框架应用于合成与真实单细胞RNA测序数据集后，我们发现现有评估指标常产生不一致的评价结果，而路径空间KL散度能实现轨迹推断方法的连贯比较，并揭示推断动力学的偏差，尤其表现在数据稀疏或缺失区域。这些结果表明，在部分可观测条件下，函数KL散度可作为评估轨迹推断的准则性指标。