Patient-Specific Probabilistic Forecasting of Alzheimer’s Disease via Conditional Flow Matching

Forecasting Alzheimer's disease progression from irregular longitudinal observations requires modeling heterogeneous future patient states at variable clinical follow-up intervals. We formulate this task as conditional probabilistic state-transition modeling and introduce a conditional flow matching framework that forecasts MRI-derived structural measures, cognitive scores, and diagnostic status. The model conditions each transition on the current patient state, elapsed clinical time, and patient-specific covariates. At inference, it samples future states and propagates them autoregressively to approximate a distribution over patient-specific trajectories from a single baseline visit. We assembled a longitudinal cohort of 1,251 Alzheimer's Disease Neuroimaging Initiative participants and evaluated forecasts at the original sparse observation times for 185 held-out participants. Against linear mixed-effects, deterministic MLP, and heteroscedastic Gaussian MLP baselines, conditional flow matching achieved the lowest patient-macro nMAE (0.0485) and nCRPS (0.0335), the highest diagnosis accuracy (0.835), and the lowest nRPS (0.0663). An individual-level analysis further demonstrated the model's utility for examining how clinical forecasts vary with APOE-$\varepsilon4$ conditioning. These results support conditional flow matching as a flexible and accurate approach for uncertainty-aware longitudinal disease forecasting.