Think on Visual Trajectories: Transferable Trajectory Recovery via Drifting

Recovering dense trajectories from sparse observations supports urban mobility analysis, commercial decision-making, and regional planning. However, reliance on city-specific road-segment vocabularies limits the transferability of many existing methods. Inspired by how human experts reconstruct journeys on maps, we investigate visual maps as a shared language for cross-city trajectory recovery: observed locations are rendered on a map, and missing movement is recovered through video generation. We construct a dataset pairing these map-rendered sparse observations with videos of the corresponding dense trajectories. Building on this formulation, we propose DriftTraj, a lightweight framework that adapts Drifting Models to map-conditioned trajectory recovery. It produces each video block in a single forward pass, avoiding iterative diffusion sampling, and recovers longer trajectories through successive blocks. Because trajectory markers occupy only a small fraction of each frame, we introduce a differentiable red-marker extractor and incorporate its spatial features into a geometric training objective, providing explicit supervision for marker location and spatial structure. We evaluate DriftTraj on Porto, Beijing, Xi'an, and Chengdu, training the generator only on Porto and transferring it to the other three cities with zero-shot transfer and limited-data fine-tuning. The results support visual maps as a shared representation for cross-city trajectory recovery and demonstrate the potential of one-step visual generation for transferable mobility modeling.