STGraphFM: Prior-Anchored Flow Matching for Joint Spatiotemporal Forecasting

Spatiotemporal forecasting requires accurate central predictions, informative uncertainty estimates, and coherent future scenarios across interacting locations. These goals call for a model that captures predictable structure while organizing variation across nodes and forecast leads. We propose STGraphFM, a prior-anchored flow-matching framework that unifies deterministic and probabilistic forecasting. A node-wise temporal prior provides a future-shaped predictive anchor, graph-correlated perturbations initialize structured alternatives around it, and a sample-dependent graph-time velocity field transports each alternative across nodes and forecast leads. Bounded velocity regression trains this field along sampled source–target paths without unrolling generation. The same learned transport maps the anchor to a central forecast and perturbed sources to complete future trajectories. Across traffic, air-quality, and gridded-temperature benchmarks, STGraphFM achieves strong point accuracy and improves probabilistic forecasts, including 18.4–45.8% lower continuous ranked probability score (CRPS) than the strongest evaluated probabilistic baselines on traffic. Matched air-quality comparisons retain joint-score gains at fixed coordinate-wise empirical marginals, providing evidence beyond marginal accuracy.