# WAM-Flow: Parallel Coarse-to-Fine Motion Planning via Discrete Flow Matching for Autonomous Driving

arXiv: https://arxiv.org/abs/2512.06112 · HTML: https://mlsanity.com/paper/2512.06112/

## Key facts

- Cited by 16 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 60 of its 65 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- End-to-end autonomous driving / [Generative simulation for driving](https://mlsanity.com/driving/generative-simulation-for-driving/)

## Builds on (most cited first, 30 of 60)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [DriveVLM: The Convergence of Autonomous Driving and Large Vision-Language Models](https://mlsanity.com/paper/2402.12289/) (2024)
- [TransFuser: Imitation with Transformer-Based Sensor Fusion for Autonomous Driving](https://mlsanity.com/paper/2205.15997/) (2022)
- [Janus: Decoupling Visual Encoding for Unified Multimodal Understanding and Generation](https://mlsanity.com/paper/2410.13848/) (2024)
- [ST-P3: End-to-end Vision-based Autonomous Driving via Spatial-Temporal Feature Learning](https://mlsanity.com/paper/2207.07601/) (2022)
- [NAVSIM: Data-Driven Non-Reactive Autonomous Vehicle Simulation and Benchmarking](https://mlsanity.com/paper/2406.15349/) (2024)
- [GPT-Driver: Learning to Drive with GPT](https://mlsanity.com/paper/2310.01415/) (2023)
- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [VADv2: End-to-End Vectorized Autonomous Driving via Probabilistic Planning](https://mlsanity.com/paper/2402.13243/) (2024)
- [NuScenes-QA: A Multi-modal Visual Question Answering Benchmark for Autonomous Driving Scenario](https://mlsanity.com/paper/2305.14836/) (2023)
- [AutoVLA: A Vision-Language-Action Model for End-to-End Autonomous Driving with Adaptive Reasoning and Reinforcement Fine-Tuning](https://mlsanity.com/paper/2506.13757/) (2025)
- [MMaDA: Multimodal Large Diffusion Language Models](https://mlsanity.com/paper/2505.15809/) (2025)
- [Is Ego Status All You Need for Open-Loop End-to-End Autonomous Driving?](https://mlsanity.com/paper/2312.03031/) (2023)
- [EMMA: End-to-End Multimodal Model for Autonomous Driving](https://mlsanity.com/paper/2410.23262/) (2024)

## Built on by (most cited first, 16 of 16)

- [EponaV2: Driving World Model with Comprehensive Future Reasoning](https://mlsanity.com/paper/2605.14696/) (2026)
- [The DAWN of World-Action Interactive Models](https://mlsanity.com/paper/2605.11550/) (2026)
- [WA-JEPA: Rethinking the Video JEPA Paradigm for World-Action Modeling in Autonomous Driving](https://mlsanity.com/paper/2608.20974/) (2026)
- [DFM-VLA: Iterative Action Refinement for Robot Manipulation via Discrete Flow Matching](https://mlsanity.com/paper/2603.26320/) (2026)
- [Discrete-WAM: Unified Discrete Vision-Action Token Editing for World-Policy Learning](https://mlsanity.com/paper/2606.05645/) (2026)
- [IDOL: Inverse-Dynamics-Guided Future Prediction for End-to-End Autonomous Driving](https://mlsanity.com/paper/2605.31476/) (2026)
- [Intend, Reflect, Refine: An Adaptive Multimodal Reflection Framework for Autonomous Driving](https://mlsanity.com/paper/2606.22913/) (2026)
- [HomoFM: Deep Homography Estimation with Flow Matching](https://mlsanity.com/paper/2601.18222/) (2026)
- [Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speech](https://mlsanity.com/paper/2605.09386/) (2026)
- [Action Emergence from Streaming Intent](https://mlsanity.com/paper/2605.12622/) (2026)
- [Driving Intents Amplify Planning-Oriented Reinforcement Learning](https://mlsanity.com/paper/2605.12625/) (2026)
- [Vision-Language Feature Alignment for Road Anomaly Segmentation](https://mlsanity.com/paper/2603.01029/) (2026)
- [A Collaborative Multi-Modality Interaction for VLA-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2608.20890/) (2026)
- [FeasibleFlow: One-Step Joint Transport of Configuration Feasibility and Trajectories for End-to-End Driving](https://mlsanity.com/paper/2609.23488/) (2026)
- [World4Scorer: Outcome-Grounded World Modeling for Autonomous Driving](https://mlsanity.com/paper/2609.36438/) (2026)
- [MORE: Learning Motion-Oriented Registers for Driving World Models and Planning](https://mlsanity.com/paper/2610.14871/) (2026)

## Abstract (arXiv)

We introduce WAM-Flow, a vision-language-action (VLA) model that casts ego-trajectory planning as discrete flow matching over a structured token space. In contrast to autoregressive decoders, WAM-Flow performs fully parallel, bidirectional denoising, enabling coarse-to-fine refinement with a tunable compute-accuracy trade-off. Specifically, the approach combines a metric-aligned numerical tokenizer that preserves scalar geometry via triplet-margin learning, a geometry-aware flow objective and a simulator-guided GRPO alignment that integrates safety, ego progress, and comfort rewards while retaining parallel generation. A multi-stage adaptation converts a pre-trained auto-regressive backbone (Janus-1.5B) from causal decoding to non-causal flow model and strengthens road-scene competence through continued multimodal pretraining. Thanks to the inherent nature of consistency model training and parallel decoding inference, WAM-Flow achieves superior closed-loop performance against autoregressive and diffusion-based VLA baselines, with 1-step inference attaining 89.1 PDMS and 5-step inference reaching 90.3 PDMS on NAVSIM v1 benchmark. These results establish discrete flow matching as a new promising paradigm for end-to-end autonomous driving. The code will be publicly available soon.