# FlowDrive: moderated flow matching with data balancing for trajectory planning

arXiv: https://arxiv.org/abs/2509.21961 · HTML: https://mlsanity.com/paper/2509.21961/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 32 of its 37 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Exploring the Limitations of Behavior Cloning for Autonomous Driving](https://mlsanity.com/paper/1904.08980/) (2019)
- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [GameFormer: Game-theoretic Modeling and Learning of Transformer-based Interactive Prediction and Planning for Autonomous Driving](https://mlsanity.com/paper/2303.05760/) (2023)
- [GoalFlow: Goal-Driven Flow Matching for Multimodal Trajectories Generation in End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.05689/) (2025)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Towards learning-based planning:The nuPlan benchmark for real-world autonomous driving](https://mlsanity.com/paper/2403.04133/) (2024)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning](https://mlsanity.com/paper/2505.22094/) (2025)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [PLUTO: Pushing the Limit of Imitation Learning-based Planning for Autonomous Driving](https://mlsanity.com/paper/2404.14327/) (2024)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following](https://mlsanity.com/paper/2402.06559/) (2024)
- [Can Vehicle Motion Planning Generalize to Realistic Long-tail Scenarios?](https://mlsanity.com/paper/2404.07569/) (2024)
- [CarPlanner: Consistent Auto-regressive Trajectory Planning for Large-scale Reinforcement Learning in Autonomous Driving](https://mlsanity.com/paper/2502.19908/) (2025)
- [Rethinking Imitation-based Planner for Autonomous Driving](https://mlsanity.com/paper/2309.10443/) (2023)
- [Plan-R1: Safe and Feasible Trajectory Planning as Language Modeling](https://mlsanity.com/paper/2505.17659/) (2025)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [Words in Motion: Extracting Interpretable Control Vectors for Motion Transformers](https://mlsanity.com/paper/2406.11624/) (2024)
- [Enhancing Autonomous Driving Safety with Collision Scenario Integration](https://mlsanity.com/paper/2503.03957/) (2025)

## Built on by (most cited first, 4 of 4)

- [Fine-tuning is Not Enough: A Parallel Framework for Collaborative Imitation and Reinforcement Learning in End-to-end Autonomous Driving](https://mlsanity.com/paper/2603.13842/) (2026)
- [FlowS: One-Step Motion Prediction via Local Transport Conditioning](https://mlsanity.com/paper/2604.26065/) (2026)
- [Learning Direct Control Policies with Flow Matching for Autonomous Driving](https://mlsanity.com/paper/2605.14832/) (2026)
- [FlowSim: Rendering-Free Closed-Loop Simulation for Evaluating End-to-End Driving Systems](https://mlsanity.com/paper/2610.18030/) (2026)

## Abstract (arXiv)

Learning-based planners are sensitive to the long-tailed distribution of driving data. Common maneuvers dominate datasets, while dangerous or rare scenarios are sparse. This imbalance can bias models toward the frequent cases and degrade performance on critical scenarios. To tackle this problem, we compare balancing strategies for sampling training data and find reweighting by trajectory pattern an effective approach. We then present FlowDrive, a flow-matching trajectory planner that learns a conditional rectified flow to map noise directly to trajectory distributions with few flow-matching steps. We further introduce moderated, in-the-loop guidance that injects small perturbation between flow steps to systematically increase trajectory diversity while remaining scene-consistent. On nuPlan and the interaction-focused interPlan benchmarks, FlowDrive achieves state-of-the-art results among learning-based planners and approaches methods with rule-based refinements. After adding moderated guidance and light post-processing (FlowDrive*), it achieves overall state-of-the-art performance across nearly all benchmark splits. Our code is available at https://github.com/einsteinguang/flow_drive_planner.