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

01TL;DR

Modern traffic simulators often look realistic but miss diverse plausible futures critical for autonomous driving.

Our Flow-ERD jointly achieves realism and diversity with agent-type-aware flow matching and entropy-regularized closed-loop distillation.

It ranks first on the WOSAC test benchmark and leads the realism–diversity Pareto front among reproducible baselines.

02Leaderboard

Realism · WOSAC 2025 Test Split

World’s #1 The world’s most realistic traffic simulator — top overall realism (RMM) on WOSAC 2025

+0.0013 Lead over 2^nd place — wider than any gap between consecutive rivals in the top 10

1^st Kinematic metric — already best with the AFM backbone alone

#	Method	RMM ↑	Kinematic ↑	Interactive ↑	Map ↑	minADE ↓
1	Flow-ERD (7M)	0.7878	0.5062	0.8110	0.9190	1.2721
2	Mhrnz	0.7865	0.4931	0.8143	0.9184	1.3051
3	SMART-tiny-DecompGAIL	0.7864	0.4919	0.8152	0.9176	1.4209
4	SMART-R1	0.7858	0.4944	0.8110	0.9201	1.2885
5	SMART-tiny-RLFTSim	0.7857	0.4927	0.8129	0.9183	1.3252
6	SMART-R1	0.7855	0.4940	0.8109	0.9194	1.2990
7	TrajTok	0.7852	0.4887	0.8116	0.9207	1.3179
8	unimotion	0.7851	0.4943	0.8105	0.9187	1.3036
9	smart-CLSFT	0.7847	0.4932	0.8104	0.9183	1.3083
10	smart-7M-catk	0.7847	0.4938	0.8101	0.9182	1.3119
11	SMART-tiny-CLSFT-RoaD	0.7847	0.4932	0.8106	0.9178	1.3042
12	smart-CLSFT	0.7847	0.4933	0.8102	0.9183	1.3101
13	SMART-tiny-CLSFT	0.7846	0.4931	0.8106	0.9177	1.3065
14	Flow Agents 7M+ ERD fine-tuning → #1	0.7845	0.4955	0.8094	0.9178	1.3358
15	MDG	0.7844	0.4928	0.8099	0.9183	1.3123

Official WOSAC 2025 test leaderboard — Flow-ERD ranks #1. Verify it live on the Waymo Open Sim Agents Challenge ↗

03Rollout gallery

Cyan = ego · white = simulated agents · all rolled out jointly in closed loop

Signalized intersections

Complex junction — queue on red, launch on green, split into diverse maneuvers.

Signal compliance — hold on red, clear on green.

Pedestrians & mixed traffic

Yielding — the ego waits out a stream of crossing pedestrians.

Mixed traffic — motorcycle and pedestrians, each with type-correct motion.

Parking areas

Front-in parking — tight, high-curvature, kinematically feasible.

Crowded lot — creeping through pedestrians between parked cars.

Highways & complex layouts

Dense highway — smooth lane-keeping over a long segment.

Complex layout — irregular topology, no off-map drift.

04Diversity

Realism–diversity Pareto front · WOSAC 2025 validation split

Realism-diversity Pareto plot: AFM traces the upper-right frontier — **Backbone:** AFM (ours) traces the upper-right frontier — no baseline reaches it under any sampling setting.

ERD beta sweep: fine-tuning lifts realism, lowering beta raises diversity — **Fine-tuned:** ERD lifts realism far above the backbone; lowering β buys even more diversity at a tiny realism cost.

Type	Method	RMM ↑	Kinematic ↑	Interactive ↑	Map ↑	CPD (diversity) ↑
Pretrained	SMART	0.7807	0.4873	0.8071	0.9144	0.1655
	TrajTok	0.7837	0.4851	0.8110	0.9193	0.1587
	UniMM	0.7812	0.4863	0.8070	0.9165	0.1514
	AFM backbone (ours)	0.7836	0.4914	0.8096	0.9172	0.1858
Fine-tuned	CAT-K (on SMART)	0.7842	0.4904	0.8110	0.9175	0.1491
	RoaD	0.7847	0.4904	0.8116	0.9182	0.1585
	RLFTSim	0.7848	0.4895	0.8116	0.9190	0.1510
	DecompGAIL	0.7854	0.4912	0.8123	0.9190	0.1420
	Flow-ERD (ours, β = 1.0)	0.7876	0.5063	0.8108	0.9184	0.1684
	Flow-ERD (ours, β = 0.99)	0.7869	0.5053	0.8099	0.9182	0.1828

Highest diversity at the highest realism — every baseline trades one for the other.

05Intent-level multimodality

Is the extra diversity meaningful, or just noise? · 64 closed-loop rollouts per scene · 1,048 WOMD validation scenes

Average per-scene intent entropy Shannon entropy of ego-intent labels, in nats · scale 0–0.5 · higher = more balanced maneuvers

SMART

0.400

Flow‑ERD β = 1.0

0.425

Flow‑ERD β = 0.99

0.477

Each ego rollout is labeled with the official WOMD trajectory-type rule; per-scene entropy is computed over the moving intents (Straight / Left / Right / U‑turn) and averaged over all 1,048 scenes. Entropy rises monotonically as β decreases.

Why RMM alone isn’t enough

RMM scores rollouts against a single logged future, so it under-rewards rare but plausible alternatives — a simulator can look perfectly realistic while collapsing onto the dominant mode. Intent entropy shows the diversity Flow-ERD preserves is semantic: distinct maneuvers available in the same scene, with the entropy temperature β acting as a direct dial between realism and mode coverage.

06Model overview

Flow-ERD architecture: AFM backbone with type-specific kinematics, ERD fine-tuning with entropy-tempered target — **(a)** AFM generates continuous actions, executed through per-type kinematics. **(b)** ERD distills the closed-loop distribution toward an entropy-tempered target that keeps minority modes alive.

07Two ingredients

AFM — Agent-Type Aware Flow Matching

Flow matching samples fine-grained continuous actions — no token codebook. Type-specific kinematics (holonomic for pedestrians, bicycle-style for vehicles and cyclists) make physically invalid motion impossible by construction.

ERD — Entropy-Regularized Distillation

Closed-loop fine-tuning with reverse-KL against an entropy-tempered target p_data^β, β ≤ 1: covariate shift is corrected while rare maneuvers — U-turns, unprotected lefts — survive instead of collapsing into the dominant mode.

08Abstract

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.

09BibTeX

@misc{hwang2026flowerd,
  title         = {Flow-ERD: Agent-type Aware Flow Matching with Entropy-Regularized
                   Distillation for Diverse Traffic Simulation},
  author        = {Hwang, Seulbin and Om, Kiyoung and Kim, Daejung and Lee, Jinhan},
  year          = {2026},
  eprint        = {2607.06957},
  archivePrefix = {arXiv},
  primaryClass  = {cs.RO},
  url           = {https://arxiv.org/abs/2607.06957}
}