  Trajectory generation and trajectory prediction are two critical tasks in
autonomous driving, which generate various trajectories for testing during
development and predict the trajectories of surrounding vehicles during
operation, respectively. In recent years, emerging data-driven deep
learning-based methods have shown great promise for these two tasks in learning
various traffic scenarios and improving average performance without assuming
physical models. However, it remains a challenging problem for these methods to
ensure that the generated/predicted trajectories are physically realistic. This
challenge arises because learning-based approaches often function as opaque
black boxes and do not adhere to physical laws. Conversely, existing
model-based methods provide physically feasible results but are constrained by
predefined model structures, limiting their capabilities to address complex
scenarios. To address the limitations of these two types of approaches, we
propose a new method that integrates kinematic knowledge into neural stochastic
differential equations (SDE) and designs a variational autoencoder based on
this latent kinematics-aware SDE (LK-SDE) to generate vehicle motions.
Experimental results demonstrate that our method significantly outperforms both
model-based and learning-based baselines in producing physically realistic and
precisely controllable vehicle trajectories. Additionally, it performs well in
predicting unobservable physical variables in the latent space.
