# Flow-ERD: Agent-type Aware Flow Matching with Entropy-Regularized Distillation for Diverse Traffic Simulation

arXiv: https://arxiv.org/abs/2607.06957 · HTML: https://mlsanity.com/paper/2607.06957/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## 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 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [TrafficSim: Learning to Simulate Realistic Multi-Agent Behaviors](https://mlsanity.com/paper/2101.06557/) (2021)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [Waymax: An Accelerated, Data-Driven Simulator for Large-Scale Autonomous Driving Research](https://mlsanity.com/paper/2310.08710/) (2023)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [The Waymo Open Sim Agents Challenge](https://mlsanity.com/paper/2305.12032/) (2023)
- [Trajeglish: Traffic Modeling as Next-Token Prediction](https://mlsanity.com/paper/2312.04535/) (2023)
- [BehaviorGPT: Smart Agent Simulation for Autonomous Driving with Next-Patch Prediction](https://mlsanity.com/paper/2405.17372/) (2024)
- [SceneDiffuser: Efficient and Controllable Driving Simulation Initialization and Rollout](https://mlsanity.com/paper/2412.12129/) (2024)
- [Closed-Loop Supervised Fine-Tuning of Tokenized Traffic Models](https://mlsanity.com/paper/2412.05334/) (2024)
- [SAFE-SIM: Safety-Critical Closed-Loop Traffic Simulation with Diffusion-Controllable Adversaries](https://mlsanity.com/paper/2401.00391/) (2023)
- [Versatile Behavior Diffusion for Generalized Traffic Agent Simulation](https://mlsanity.com/paper/2404.02524/) (2024)
- [KiGRAS: Kinematic-Driven Generative Model for Realistic Agent Simulation](https://mlsanity.com/paper/2407.12940/) (2024)
- [Advancing Multi-agent Traffic Simulation via R1-Style Reinforcement Fine-Tuning](https://mlsanity.com/paper/2509.23993/) (2025)
- [Decoupled Diffusion Sparks Adaptive Scene Generation](https://mlsanity.com/paper/2504.10485/) (2025)
- [LANGTRAJ: Diffusion Model and Dataset for Language-Conditioned Trajectory Simulation](https://mlsanity.com/paper/2504.11521/) (2025)
- [Guaranteeing Consistency in a Motion Planning and Control Architecture Using a Kinematic Bicycle Model](https://mlsanity.com/paper/1804.08290/) (2018)
- [RoaD: Rollouts as Demonstrations for Closed-Loop Supervised Fine-Tuning of Autonomous Driving Policies](https://mlsanity.com/paper/2512.01993/) (2025)
- [DecompGAIL: Learning Realistic Traffic Behaviors with Decomposed Multi-Agent Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2510.06913/) (2025)
- [MDG: Masked Denoising Generation for Multi-Agent Behavior Modeling in Traffic Environments](https://mlsanity.com/paper/2511.17496/) (2025)

## Abstract (arXiv)

Realistic and diverse traffic simulation is essential to autonomous driving development. Yet prevailing benchmarks predominantly reward realism, and recent methods have optimized accordingly, leaving diversity underexplored. We introduce Flow-ERD, a multi-agent simulator that pursues realism and diversity jointly. Its backbone, Agent-Type Aware Flow Matching (AFM), couples flow matching's multi-modal expressiveness with type-specific kinematic execution. It preserves fine-grained diversity while keeping motions consistent with each agent type. A second stage, Entropy-Regularized Distillation (ERD), fine-tunes the closed-loop rollout distribution with an entropy-regularized reverse-KL objective. This mitigates covariate shift while explicitly preventing collapse onto high-density modes. We evaluate Flow-ERD with a log-free diversity metric alongside standard realism scores. Flow-ERD ranks first on the WOSAC test benchmark and dominates the realism--diversity Pareto front among reproducible baselines. Our project page is available hrefhttps://seulbinhwang.github.io/flow-erd-project-page/here.