Predicting how a dynamical unit evolves over time - how an individual ages, an epidemic spreads, or a physical system degrades - typically requires dense longitudinal tracking. When only extremely sparse or entirely cross-sectional data is available, inferring individualized, continuous-time trajectories is fundamentally ill-posed. Existing methods force a strict compromise: sequence models (e.g. latent ODEs) require dense longitudinal data, while cross-sectional methods (e.g. optimal transport, flow matching-based) map aggregate populations, losing individual dynamics. In this paper, we demonstrate that this dichotomy can be broken. We introduce CADENCE, a principled probabilistic framework that recovers continuous individual trajectories from isolated snapshots by anchoring latent dynamics to static, individual-level contexts. We provide novel identifiability guarantees for single-timepoint trajectory inference. By combining a score-based spatial encoder (bijective Probability Flow ODE) to eliminate diffeomorphic ambiguities with a Soft Mixture-of-Experts (SMoE) router, we show that individual dynamical parameters and routing function are jointly identifiable. Across a suite of benchmarks spanning physical systems to real-world biological data, CADENCE, trained strictly on extremely sparse snapshots with context structure, matches or exceeds the performance of state-of-the-art sequential models trained on dense, full-trajectory data.

翻译：预测一个动态单元随时间如何演化——例如个体如何衰老、流行病如何传播或物理系统如何退化——通常需要密集的纵向追踪。当仅能获得极端稀疏或完全横截面的数据时，推断个体化的连续时间轨迹本质上是不适定的。现有方法迫使一种严格折衷：序列模型（如潜在常微分方程）需要密集纵向数据，而横截面方法（如最优传输、基于流匹配的方法）则映射总体分布，从而丢失个体动态。在本文中，我们证明这一两难困境可以被打破。我们提出CADENCE，一个基于原则的概率框架，通过将潜在动态锚定于静态的个体级上下文，从孤立快照中恢复连续个体轨迹。我们为单时间点轨迹推断提供了新的可辨识性保证。通过结合基于分数的空间编码器（双射概率流常微分方程）以消除微分同胚歧义，与软专家混合路由器，我们展示了个体动态参数和路由函数可联合辨识。在一系列涵盖物理系统到真实世界生物数据的基准测试中，CADENCE严格基于具有上下文结构的极端稀疏快照进行训练，其性能匹敌甚至超越了在密集全轨迹数据上训练的最先进序列模型。