From Sparse Visits to Continuous Molecular Trajectories with Flow Matching

Longitudinal transcriptomic studies often capture only a few molecular snapshots of each patient over time. This makes it challenging to understand how patients are progressing, compare them when progression rates differ, and capture molecular changes between observed visits. We introduce CohortFM, a flow-matching framework that reconstructs continuous patient-specific molecular trajectories from sparse longitudinal observations and organizes them through an integrated mixture model into a compact set of cohort-level progression patterns. CohortFM separates molecular progression from calendar time, places patients on a shared progression scale, uses observed intermediate states to guide the learned trajectories, and maps the resulting patterns back to real patient samples for biological interpretation. We evaluated CohortFM across COVID-19, sepsis, influenza, and tuberculosis. Despite different sampling patterns, the method generalizes well and consistently produces meaningful trajectories. These trajectories capture biological differences between patients that cannot be explained by the observed samples alone. Compared with state-of-the-art trajectory baselines, CohortFM produces more biologically distinct trajectories and a more complete representation of the patient population. Its finer progression scale also reveals biological programs and temporal dynamics that are not captured by visit-level analysis. We further evaluated interpolation and true forward prediction to test whether CohortFM can accurately recover unobserved states. CohortFM remains competitive with strong interpolation baselines and is among the strongest learned predictors in the harder forecasting setting. Ablation experiments further show that flow matching is the core learning mechanism and that our design choices improve continuous trajectory learning. Our results support CohortFM as a practical framework for turning sparse molecular snapshots into continuous, biologically interpretable trajectories. By going beyond visit labels, CohortFM makes it possible to study disease progression and predict future molecular states even when patients are sampled only a few times.