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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-","title":"Learning Individual Dynamics from Sparse Cross-Sectional Snapshots","url":"https://arxiv.org/abs/2605.23470","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.23470v1 Announce Type: cross \nAbstract: 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. 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