GeoDiffusion: Spatio-Temporal Offset-Aware Latent Diffusion for Irregular Trajectories

Real-world spatio-temporal sequences often consist of irregularly sampled trajectory observations, where spatial displacements are coupled with unequal time intervals, creating a mismatch between sequence adjacency and the scale of physical transitions. This challenges a basic assumption of standard sequence modeling: adjacent tokens correspond to directly comparable physical transitions. Sequence indices alone cannot distinguish these transition scales. To address this problem, we propose GeoDiffusion, a spatio-temporal offset-aware latent diffusion framework that builds on diffusion models’ ability to model joint trajectory distributions. Specifically, spatio-temporal offset encoding jointly embeds the spatial displacement and time interval between consecutive observations. Learnable latent queries then aggregate position and offset features, enabling the denoising network to reconstruct latent representations that incorporate both trajectory locations and transition scales. Derived from the trajectories themselves, the offset features provide a transition-oriented inductive bias. Experiments on five maritime and urban trajectory datasets show favorable aggregate prediction and imputation performance across the evaluated settings, with exceptions in individual comparisons. Jaccard comparisons and averaged POR, DTW, and ADE measurements characterize visited-grid overlap, sequence alignment, and coordinate accuracy.