# Guiding End-to-End Driving Models with Endpoint-Constrained Trajectory Optimization

arXiv: https://arxiv.org/abs/2609.31383 · HTML: https://mlsanity.com/paper/2609.31383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving.
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Placed in

- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)

## Builds on (most cited first, 30 of 33)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [VAD: Vectorized Scene Representation for Efficient Autonomous Driving](https://mlsanity.com/paper/2303.12077/) (2023)
- [KITTI-360: A Novel Dataset and Benchmarks for Urban Scene Understanding in 2D and 3D](https://mlsanity.com/paper/2109.13410/) (2021)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [TransFuser: Imitation with Transformer-Based Sensor Fusion for Autonomous Driving](https://mlsanity.com/paper/2205.15997/) (2022)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Hydra-MDP: End-to-end Multimodal Planning with Multi-target Hydra-Distillation](https://mlsanity.com/paper/2406.06978/) (2024)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [PandaSet: Advanced Sensor Suite Dataset for Autonomous Driving](https://mlsanity.com/paper/2112.12610/) (2021)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [GenAD: Generalized Predictive Model for Autonomous Driving](https://mlsanity.com/paper/2403.09630/) (2024)
- [Hidden Biases of End-to-End Driving Models](https://mlsanity.com/paper/2306.07957/) (2023)
- [HUGSIM: A Real-Time, Photo-Realistic and Closed-Loop Simulator for Autonomous Driving](https://mlsanity.com/paper/2412.01718/) (2024)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [SafetyNet: Safe planning for real-world self-driving vehicles using machine-learned policies](https://mlsanity.com/paper/2109.13602/) (2021)
- [On Offline Evaluation of Vision-based Driving Models](https://mlsanity.com/paper/1809.04843/) (2018)
- [Driving on Registers](https://mlsanity.com/paper/2601.05083/) (2026)
- [Hydra-NeXt: Robust Closed-Loop Driving with Open-Loop Training](https://mlsanity.com/paper/2503.12030/) (2025)
- [SimScale: Learning to Drive via Real-World Simulation at Scale](https://mlsanity.com/paper/2511.23369/) (2025)
- [VaViM and VaVAM: Autonomous Driving through Video Generative Modeling](https://mlsanity.com/paper/2502.15672/) (2025)

## Abstract (arXiv)

End-to-end driving policies are commonly trained through open-loop behavior cloning, yet they must ultimately operate in closed-loop when deployed on a vehicle, creating a fundamental mismatch between training and execution. Beyond the commonly studied effects of covariate shift and causal confusion, we identify a complementary factor for this open-loop/closed-loop gap: waypoint-based supervision and displacement metrics do not ensure that the intermediate trajectory is physically coherent or easy for the controller to track. We observe that these inconsistencies concentrate primarily at intermediate waypoints, while the predicted endpoint remains comparatively reliable. Based on this observation, we introduce Endpoint-Constrained Optimization (ECO), a lightweight postprocessing layer that anchors the trajectory to the vehicle's executed history, preserves the policy's predicted endpoint, and reshapes the intermediate waypoints to improve feasibility. ECO requires no map, privileged simulator state, or additional training, and can be inserted between a broad range of waypoint-emitting policies and their controllers. Across two closed-loop simulators, it improves the aggregate closed-loop score of all six evaluated generative and regression-based driving policies, and the gains tend to increase with how often the base plans violate motion limits. On HUGSIM, ECO improves VaVAM from 18.1 to 31.0 HD-Score (+71%), achieving 1st place on the HUGSIM Closed-Loop Driving Challenge. Similarly, on AlpaSim, ECO increases the scene scores of VaVAM and DiffusionDrive by 123% and 22%, respectively. These results show that for a broad collection of end-to-end driving models, repairing the intermediate geometry of predicted trajectories without changing the policy's predicted endpoint can substantially improve closed-loop performance.