$SE(2)$-Aware Conditional Distribution Transport for Vehicle Trajectory Generation

Vehicle trajectory generation is critical for autonomous driving simulation. However, current generative models face two coupled limitations: (i) imbalanced trajectory distributions bias them toward frequent motions, such as straight driving or stationary states, while weakening their ability to synthesize rare but safety critical motions, such as turning. (ii) Euclidean intermediate spaces provide limited geometric inductive bias for modeling vehicle pose evolution. Together, these limitations lead to mode biased generation and physically less coherent trajectories. To address this issue, we propose SEA, an \underline{\textbf{SE}}(2)-\underline{\textbf{A}}ware vehicle trajectory generation method that realizes the conditional transport path through planar rigid body poses. At the \textbf{data distribution} level, SEA learns vehicle trajectory distributions from traffic data to capture individual motion characteristics. At the \textbf{physical-space} level, motivated by the geometry dependence of {\bf optimal transport} interpolation, SEA realizes intermediate transport states through an $SE(2)$-consistent construction, thereby preserving geometric interpretability and physical coherence during generation. Extensive experiments on large scale real world datasets show that our method outperforms state of the art approaches by generating more realistic, diverse and dynamically consistent trajectories.