# Diverse Multiple Trajectory Prediction Using a Two-stage Prediction Network Trained with Lane Loss

arXiv: https://arxiv.org/abs/2206.08641 · HTML: https://mlsanity.com/paper/2206.08641/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 39 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (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)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Multimodal Motion Prediction with Stacked Transformers](https://mlsanity.com/paper/2103.11624/) (2021)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Prediction](https://mlsanity.com/paper/2104.00563/) (2021)
- [HOME: Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2105.10968/) (2021)
- [LaneRCNN: Distributed Representations for Graph-Centric Motion Forecasting](https://mlsanity.com/paper/2101.06653/) (2021)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Diverse Trajectory Forecasting with Determinantal Point Processes](https://mlsanity.com/paper/1907.04967/) (2019)
- [TPNet: Trajectory Proposal Network for Motion Prediction](https://mlsanity.com/paper/2004.12255/) (2020)
- [What-If Motion Prediction for Autonomous Driving](https://mlsanity.com/paper/2008.10587/) (2020)
- [Diverse and Admissible Trajectory Forecasting through Multimodal Context Understanding](https://mlsanity.com/paper/2003.03212/) (2020)
- [LaPred: Lane-Aware Prediction of Multi-Modal Future Trajectories of Dynamic Agents](https://mlsanity.com/paper/2104.00249/) (2021)
- [Learning to Predict Vehicle Trajectories with Model-based Planning](https://mlsanity.com/paper/2103.04027/) (2021)
- [DiversityGAN: Diversity-Aware Vehicle Motion Prediction via Latent Semantic Sampling](https://mlsanity.com/paper/1911.12736/) (2019)
- [Divide-and-Conquer for Lane-Aware Diverse Trajectory Prediction](https://mlsanity.com/paper/2104.08277/) (2021)
- [Analyzing the Variety Loss in the Context of Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1907.10178/) (2019)
- [Trajectory Prediction in Autonomous Driving with a Lane Heading Auxiliary Loss](https://mlsanity.com/paper/2011.06679/) (2020)
- [Probabilistic Multi-modal Trajectory Prediction with Lane Attention for Autonomous Vehicles](https://mlsanity.com/paper/2007.02574/) (2020)

## Built on by (most cited first, 12 of 12)

- [Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following](https://mlsanity.com/paper/2402.06559/) (2024)
- [Machine Learning for Autonomous Vehicle's Trajectory Prediction: A comprehensive survey, Challenges, and Future Research Directions](https://mlsanity.com/paper/2307.07527/) (2023)
- [Vision-based Multi-future Trajectory Prediction: A Survey](https://mlsanity.com/paper/2302.10463/) (2023)
- [Diverse Controllable Diffusion Policy with Signal Temporal Logic](https://mlsanity.com/paper/2503.02924/) (2025)
- [Multi-Agent Trajectory Prediction with Difficulty-Guided Feature Enhancement Network](https://mlsanity.com/paper/2407.18551/) (2024)
- [MS-Net: A Multi-Path Sparse Model for Motion Prediction in Multi-Scenes](https://mlsanity.com/paper/2403.00353/) (2024)
- [Efficient Baselines for Motion Prediction in Autonomous Driving](https://mlsanity.com/paper/2309.03387/) (2023)
- [ProIn: Learning to Predict Trajectory Based on Progressive Interactions for Autonomous Driving](https://mlsanity.com/paper/2403.16374/) (2024)
- [Perception Without Vision for Trajectory Prediction: Ego Vehicle Dynamics as Scene Representation for Efficient Active Learning in Autonomous Driving](https://mlsanity.com/paper/2405.09049/) (2024)
- [Marginalized Generalized IoU (MGIoU): A Unified Objective Function for Optimizing Any Convex Parametric Shapes](https://mlsanity.com/paper/2504.16443/) (2025)
- [Dynamic Risk Assessment for Autonomous Vehicles from Spatio-Temporal Probabilistic Occupancy Heatmaps](https://mlsanity.com/paper/2501.16480/) (2025)
- [Adjustment of Cluster-Then-Predict Framework for Multiport Scatterer Load Prediction](https://mlsanity.com/paper/2602.08129/) (2026)

## Abstract (arXiv)

Prior arts in the field of motion predictions for autonomous driving tend to focus on finding a trajectory that is close to the ground truth trajectory. Such problem formulations and approaches, however, frequently lead to loss of diversity and biased trajectory predictions. Therefore, they are unsuitable for real-world autonomous driving where diverse and road-dependent multimodal trajectory predictions are critical for safety. To this end, this study proposes a novel loss function, textitLane Loss, that ensures map-adaptive diversity and accommodates geometric constraints. A two-stage trajectory prediction architecture with a novel trajectory candidate proposal module, textitTrajectory Prediction Attention (TPA), is trained with Lane Loss encourages multiple trajectories to be diversely distributed, covering feasible maneuvers in a map-aware manner. Furthermore, considering that the existing trajectory performance metrics are focusing on evaluating the accuracy based on the ground truth future trajectory, a quantitative evaluation metric is also suggested to evaluate the diversity of predicted multiple trajectories. The experiments performed on the Argoverse dataset show that the proposed method significantly improves the diversity of the predicted trajectories without sacrificing the prediction accuracy.