# PhysVarMix: Physics-Informed Variational Mixture Model for Multi-Modal Trajectory Prediction

arXiv: https://arxiv.org/abs/2507.19701 · HTML: https://mlsanity.com/paper/2507.19701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [One Thousand and One Hours: Self-driving Motion Prediction Dataset](https://mlsanity.com/paper/2006.14480/) (2020)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Prediction](https://mlsanity.com/paper/2104.00563/) (2021)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)
- [Probabilistic Multi-modal Trajectory Prediction with Lane Attention for Autonomous Vehicles](https://mlsanity.com/paper/2007.02574/) (2020)
- [Towards a Functional System Architecture for Automated Vehicles](https://mlsanity.com/paper/1703.08557/) (2017)
- [Navigation under uncertainty: Trajectory prediction and occlusion reasoning with switching dynamical systems](https://mlsanity.com/paper/2410.10653/) (2024)

## Abstract (arXiv)

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.