Learning Individual Dynamics from Sparse Cross-Sectional Snapshots

Forecasting how an individual unit, such as a patient, a community or a machine, will evolve usually requires repeated measurements of that unit, yet many datasets are cross-sectional: many units, each observed once. Sequence models need the per-unit sequences such data lack, while optimal transport and flow matching describe the population rather than the individual. We introduce CADENCE, which forecasts individual continuous-time trajectories from a single observation per unit by anchoring latent dynamics to static context. A score-based encoder maps observations into a latent space with a fixed Gaussian marginal, and a context-routed mixture of experts blends a shared basis of dynamical archetypes into the per-unit parameters of a latent neural ODE, trained by matching per-subgroup marginals across units. We show that marginal matching alone cannot identify individual dynamics, and give structural conditions under which the per-subgroup dynamics are identifiable within a fixed encoder frame; these conditions motivate the design. On six synthetic benchmarks, CADENCE attains the lowest individual-level error among published cross-sectional methods on five and the highest per-unit skill on all six, while conditional transport trained on full trajectories remains more accurate where such data exist. On real-world lineage-traced haematopoiesis data, trained on day-2 cells and unlabelled later-day populations without lineage or fate labels, CADENCE achieves strongest clonal fate predictions with AUROC $0.82$, above published unsupervised dynamics methods ($0.71$-$0.78$).