Non-parametric spatiotemporal trajectory prediction via state-conditioned transition sampling

We present a nonparametric method for multi-modal trajectory prediction that requires no GPU, fits in seconds on CPU, and matches or exceeds a 57M-parameter transformer. The method builds a transition table of historical state-to-next-position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces multiple trajectories covering distinct plausible routes, while beam search finds the single highest-likelihood path. On the TrAISformer benchmark (Danish Maritime Authority AIS, 1,481 test trajectories), our beam search achieves 9.13 km top-1 ADE at 3 hours (vs. 9.51 km for TrAISformer argmax) and our diverse sampling achieves 2.38 km best-of-16 ADE (vs. 2.80 km for TrAISformer sampling). In data-scarce regimes, our method outperforms the transformer by 2–4× and remains stable down to 2% of training data where TrAISformer degrades catastrophically. The method requires zero learned parameters, works immediately on new regions given sufficient historical data, and provides interpretable predictions grounded in observed transitions.