Accurate prediction of future agent trajectories is a critical challenge for ensuring safe and efficient autonomous navigation, particularly in complex urban environments characterized by multiple plausible future scenarios. In this paper, we present a novel hybrid approach that integrates learning-based with physics-based constraints to address the multi-modality inherent in trajectory prediction. Our method employs a variational Bayesian mixture model to effectively capture the diverse range of potential future behaviors, moving beyond traditional unimodal assumptions. Unlike prior approaches that predominantly treat trajectory prediction as a data-driven regression task, our framework incorporates physical realism through sector-specific boundary conditions and Model Predictive Control (MPC)-based smoothing. These constraints ensure that predicted trajectories are not only data-consistent but also physically plausible, adhering to kinematic and dynamic principles. Furthermore, our method produces interpretable and diverse trajectory predictions, enabling enhanced downstream decision-making and planning in autonomous driving systems. We evaluate our approach on two benchmark datasets, demonstrating superior performance compared to existing methods. Comprehensive ablation studies validate the contributions of each component and highlight their synergistic impact on prediction accuracy and reliability. By balancing data-driven insights with physics-informed constraints, our approach offers a robust and scalable solution for navigating the uncertainties of real-world urban environments.