Gaussian Mixture Conditional Variational Recurrent Neural Network for Unified Trajectory Imputation and Prediction

Predicting trajectories is essential for interpreting human behavior, yet it remains a challenging task when relying solely on observed motion patterns. Despite substantial progress, most existing methods assume fully observed trajectories and fail to account for missing data caused by occlusion, limited field of view, or sensor failures. This limitation substantially compromises the reliability of trajectory prediction, particularly in real-world deployment where observations are often incomplete. In light of this issue, our work presents the Gaussian Mixture Conditional Variational Recurrent Neural Network (GMC-VRNN), which unifies trajectory imputation and prediction within a single framework. Our GMC-VRNN framework couples a Multi-Space Graph Neural Network (MS-GNN) with a Gaussian Mixture Conditional VRNN, further augmented by a Bidirectional Temporal Decay (BTD) module, to achieve robust spatio-temporal representation learning under incomplete observations. To verify its effectiveness, we conduct extensive evaluations on two sports datasets covering multiple scenarios, jointly tackling trajectory imputation and prediction. Our experiments confirm that GMC-VRNN surpasses recent state-of-the-art approaches, offering enhanced precision and stronger robustness under diverse conditions.