TrajCFM: Observation-Conditioned Flow Matching for Unified Trajectory Modeling

Real-world trajectories combine irregular sampling, partial observability, and heterogeneous motion dynamics. Modeling them across tasks requires capturing local motion structure under different observation conditions. We present TrajCFM, an observation-conditioned flow matching framework for unified trajectory modeling. A DiT-style Transformer, conditioned on flow time and observed trajectory context, learns a velocity field that transports noise at unobserved positions toward target coordinates while preserving observed locations. This formulation brings completion and prediction under a shared objective and backbone. To capture motion at varying temporal scales, observation-aware adaptive patching builds variable-length segment representations from local motion cues and observation availability. Sparse mixture-of-experts routing selectively activates experts to model heterogeneous trajectory patterns. Pretraining with diverse observation masks learns representations that can also be adapted to trajectory classification and road-conditioned generation. Experiments on five real-world datasets demonstrate that TrajCFM achieves state-of-the-art performance in both trajectory completion and prediction using only three flow integration steps. Downstream experiments on transport-mode classification across GeoLife and Grab-Posisi, together with road-conditioned generation, demonstrate the transferability of the learned representations.