Closed-loop evaluation of autonomous-driving policies requires interactive simulation beyond log replay. However, existing generative world models often degrade in closed loop due to (i) history-free initialization that mismatches policy inputs, (ii) multi-step sampling latency that violates real-time budgets, and (iii) compounding kinematic infeasibility over long horizons. We propose VectorWorld, a streaming world model that incrementally generates ego-centric 64m×64m lane--agent vector-graph tiles during rollout. VectorWorld aligns initialization with history-conditioned policies by producing a policy-compatible interaction state via a motion-aware gated VAE. It enables real-time outpainting via solver-free one-step masked completion with an edge-gated relational DiT trained with interval-conditioned MeanFlow and JVP-based large-step supervision. To stabilize long-horizon rollouts, we introduce ΔSim, a physics-aligned non-ego (NPC) policy with hybrid discrete--continuous actions and differentiable kinematic logit shaping. On Waymo open motion and nuPlan, VectorWorld improves map-structure fidelity and initialization validity, and supports stable, real-time 1km+ closed-loop rollouts (code).
Figures & tables
Figure 1: Comparison with Prior Works. Unlike prior pipelines that degrade in closed loop due to accumulated drift (autoregressive rollout) or history-free cold-start initialization, VectorWorldsupports kilometer-scale closed-loop simulation via streaming outpainting in our experiments. The engine operates in a closed loop: 0) An Ego Planner drives within the scene; 1) Initial Scene Generation creates the base tile; 2) Scene Outpainting dynamically extends the map frontier using edge-gated relational DiT; and 3) NPC Behavior ( Δ Sim) ensures reactive interactions. This mechanism enables consistent, kilometer-scale driving simulation by progressively outpainting the world ahead.
Figure 2: Interaction-state interface with motion-aware gated VAE. A motion-aware gate gi fuses static state si and motion code mi , suppressing history noise for stationary agents while preserving dynamics for moving ones. A factorized scene transformer aggregates typed relations (L2L/L2A/A2A) and outputs Gaussian latents z=(zlane,zagent) for downstream generation. Warm-started interaction states align initialization with history-conditioned policies.
Figure 3: Edge-gated relational DiT for vector-graph latent generation. The framework generates vector-graph latents via a factorized transformer backbone. To capture complex graph dependencies, we introduce a Relational Attention Module (Right). Unlike standard attention, this module conditions message passing on edge features eij via: 1) An additive bias Bij applied to attention scores to regulate connectivity; 2) A multiplicative gate Gij applied to value vectors to modulate feature aggregation. This design enables precise structural control across heterogeneous agents and map elements, compatible with various generative dynamics (DDPM, Flow, or MeanFlow).
Figure 4: Δ Sim: physics-aligned NPC policy. A single-pass return-to-go (RTG) control embedding modulates the decoder via FiLM (γ,β) . Actions use a hybrid head (discrete k-disks token plus continuous residual) with differentiable kinematic logit shaping and DKAL regularization. This design reduces feasibility violations that compound under kilometer-scale closed-loop simulation.
Dataset
Method
Perceptual
Map Structure
Safety
FD ↓
Route Len. (m) ↑
Endpt. Dist. (m) ↓
Coll. Rate (%) ↓
nuPlan
SLEDGE-L ( Chitta et al., 2024 )
1.89
35.34 ± 8.63
0.470 ± 0.320
22.30
SLEDGE-XL ( Chitta et al., 2024 )
1.44
35.83 ± 8.35
0.420 ± 0.290
21.20
ScenDream-B ( Rowe et al., 2025 )
1.05
37.04 ± 10.21
0.320 ± 0.800
11.90
ScenDream-L ( Rowe et al., 2025 )
0.67
36.87 ± 10.37
0.250 ± 0.710
9.30
VectorWorld (Ours)
0.98
37.22 ± 11.40
0.078 ± 0.106
3.01
Table 1: Quantitative comparison of scene generation quality. We evaluate VectorWorld against prior vectorized scene generators on nuPlan and Waymo. VectorWorld achieves strong structure and safety with competitive perceptual alignment. ↓ / ↑ indicates lower/higher is better. Bold and underline denote the best and second-best results among non-privileged methods.
Figure 5: Qualitative comparison on Waymo and nuPlan. Visualizing decoded elements in 64m×64m tiles. VectorWorld demonstrates superior lane connectivity and fewer agent overlaps at initialization compared to prior vectorized generators.
Figure 6: Quality–latency trade-off for tile generation. Endpoint distance (EPD) and mean agent-JSD are plotted against wall-clock latency as the solver-step budget varies; the vertical marker indicates the streaming budget (including one VAE decode).
Simulator
NPC Policy
Ego Planner
Sys. Cap.
Scene Val.
Ego Performance
Dyn. Metric
Online
Warm
FD ↓
S.Coll ↓
Coll.
Off.
Succ.
Route (m)
Value
I. Platform Stability & Consistency (Goal: Verify simulation realism using a standard IDM driver ( Treiber et al., 2000 ) .)
Waymo
Replay
IDM (Rule-based)
✗
✗
0.00
–
7.2
5.8
87.0
64
11.4 (Jerk)
ScenDream-L
Ctrl-sim
IDM (Rule-based)
✗
✗
1.38
4.80
12.4
5.9
81.7
200
15.5 (Jerk)
VectorWorld
Δ Sim
IDM (Rule-based)
✗
✗
1.05
4.69
7.5
1.5
91.0
200
10.4 (Jerk)
VectorWorld
Δ Sim
IDM (Rule-based)
✓
✗
1.19
7.39
45.5
6.9
47.6
1000
16.6 (Jerk)
Table 2: Closed-loop system evaluation on Waymo. Units: Scene Validity (FD, S.Coll) and Ego Performance (Coll, Offroad, Success) are in percentages (%) unless unitless. Route is in meters. Columns: NPC Policy denotes the background traffic controller; Ego Planner denotes the agent under test. Key: Warm = Motion-history warm start; Online = Streaming outpainting.
Method
Components
Acc.
Ctrl.
Effic.
RTG
A+R
DKAL
ADE ↓
ρ↑
Lat. ↓
Fwd ↓
Ctrl-Sim ( Rowe et al., 2024 )
✗
✗
✗
2.80
-0.25
36.9
2.0
Δ Sim (w/o Refine)
✓
✗
✓
2.62
0.39
21.7
1.0
Δ Sim (w/o DKAL)
✓
✓
✗
2.10
0.24
26.1
1.0
Δ Sim (Ours)
✓
✓
✓
1.72
0.53
26.1
1.0
Table 3: Δ Sim ablation on Waymo. Components: return-to-go conditioning (RTG), hybrid anchor+residual action head (A+R), and DKAL. Metrics: average displacement error (ADE; ↓ ), controllability rank-correlation ( ρ ; ↑ ), and inference cost (latency / forward passes; ↓ ).
Appendix figures & tables21 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Type / shape
Meaning
G=(V,E)
set-valued
Heterogeneous lane–agent vector graph for one ego-centric tile.
Vlane,Vagent
sets
Lane nodes / agent nodes in G .
Nℓ
integer
Number of lane segments in a scene (capped by Nℓmax ).
Na
integer
Number of agents in a scene (capped by Namax ; includes ego).
P
integer
Number of points per lane polyline for the generator/autoencoder ( P=20 in Waymo generation).
PΔ
integer
Number of points per lane polyline for Δ Sim context ( PΔ=50 in Waymo behavior).
Appendix
Table 4: Core notation for the vectorized scene representation (per scene unless stated otherwise).
Symbol
Type / shape
Meaning
Encϕ
function
VAE encoder mapping a scene graph to Gaussian posterior parameters.
Decψ
function
VAE decoder mapping sampled latents to reconstructed scene elements.
zℓ
RNℓ×dℓ
Lane latents (Waymo: dℓ=24 ).
za
RNa×da
Agent latents (Waymo: da=18 ).
z
R(⋅)
Concatenated latents, z=(zℓ,za) .
zt
R(⋅)
Noisy latent on the rectified path at time t : zt=(1−t)z+tϵ .
Appendix
Table 5: Notation for latent variables and generative dynamics (VAE + diffusion/flow/MeanFlow).
Symbol
Type / shape
Meaning
πego
policy
Ego planner/policy used in closed-loop rollout.
πΔ
policy
NPC policy implemented by Δ Sim.
R
scalar
Tile radius (ego-centered observation crop) used by the simulator.
τ
scalar
Outpainting trigger distance to the tile boundary (Algorithm 2 ).
Vkd
RKkd×3
k-disks vocabulary of SE(2) deltas, (Δx,Δy,Δθ) , with Kkd=384 .
ak
integer
Discrete action token index at simulation step k .
Appendix
Table 6: Notation for the Δ Sim behavior model and closed-loop simulation.
Figure 7: Visualization of motion-aware gating (Waymo). Gate activation increases with motion magnitude, clustering static agents at low activation while assigning higher activation to dynamic agents. This supports that the motion-aware gated VAE suppresses motion-code noise for parked agents while encoding history for moving agents, improving warm-start consistency.
Hyperparameter
Motion-aware VAE
MeanFlow latent generator
Δ Sim behavior model
Optimizer
AdamW
AdamW
AdamW
Base learning rate
1.0×10−4
1.0×10−4
6.0×10−5
β1,β2
(0.9,0.999)
(0.9,0.999)
(0.9,0.999)
ϵ
1.0×10−7
1.0×10−7
1.0×10−7
Weight decay
2.0×10−5
1.0×10−5
1.0×10−4
Training length
60,000 steps
100,000 steps
10,000 steps
Appendix
Table 7: Training hyperparameters on Waymo. Values are reported for the default setting used in our main experiments.
Dataset
Method
Topology ↓
Agent Distributional JSD ↓
Conn.
Dens.
Reach
Conve.
Near.
Lat.
Ang.
Len.
Wid.
Speed
Count
nuPlan
SLEDGE-L ( Chitta et al., 2024 )
2.34
2.43
0.70
2.44
0.53
0.63
3.60
11.84
10.16
0.46
0.109
SLEDGE-XL ( Chitta et al., 2024 )
1.67
1.74
0.51
1.68
0.49
0.49
3.26
11.16
10.29
0.47
0.217
ScenDream-B ( Rowe et al., 2025 )
0.28
0.45
0.07
0.14
0.12
0.15
0.17
0.22
0.14
0.07
0.023
ScenDream-L ( Rowe et al., 2025 )
0.18
0.43
0.03
0.33
0.09
0.11
0.18
0.25
0.17
0.06
0.011
Ours
0.09
0.41
0.09
0.79
0.26
0.31
0.18
0.35
0.22
0.07
0.004
Appendix
Table 8: Evaluation of map topology and agent distribution alignment. We report lane-graph Topology discrepancies (Conn., Dens., Reach, Conve.; lower is better) and Agent Distributional JSD for key attributes (lower is better). These metrics diagnose structural and density drifts that can be amplified under repeated inpainting/outpainting. Bold and underline denote the best and second-best results among non-privileged methods (excluding methods marked with * ).
VAE variant
Interface components
Autoencoding
Downstream init.
Motion code
Motion gate
Factorized scene tr.
Count prior
Static L1 ↓
Motion L1 ↓
KL ↓
EPD (m) ↓
Init coll. (%) ↓
Snapshot-only
✗
✗
✓
✓
0.012
–
5.23
0.120
9.45
Concat motion (no gate)
✓
✗
✓
✓
0.017
0.045
4.99
0.102
4.92
Gated
✓
✓
✓
✓
0.011
0.042
4.63
0.098
4.85
motion-aware gated VAE (ours)
✓
✓
✓
✓
0.008
0.038
4.37
0.094
4.69
Additional interface checks
Appendix
Table 9: Ablations of motion-aware gated VAE (Waymo). We evaluate the impact of the interaction-state interface on autoencoding fidelity and downstream initialization. Snapshot-only leads to high initialization collision rates due to the lack of motion history (cold start). Concat motion (naive) degrades static reconstruction by injecting noise into parked vehicles. Our Motion-aware Gated design achieves the best trade-off, selectively encoding momentum only for dynamic agents. Lower is better for all metrics.
Variant
Relation-aware modules
Perceptual
Map structure
Safety
Agent distributional JSD ↓
Rel. bias
Value gate
Cross-type bias
Global fusion
FD ↓
RouteLen. (m) ↑
Endpt. dist. (m) ↓
Route valid. (%) ↑
Coll. rate (%) ↓
Near.
Ang.
Len.
Wid.
Speed
Factorized DiT (Base)
✗
✗
✗
✗
1.53
35.26
0.301
87.36
6.53
0.12
0.09
0.51
0.29
0.39
+ Relational logit bias
✓
✗
✗
✗
1.35
37.10
0.185
92.10
5.80
0.11
0.09
0.42
0.25
0.35
+ Edge-gated values
✓
✓
✗
✗
1.20
37.85
0.142
94.50
5.12
0.10
0.08
0.30
0.18
0.28
+ Cross-type rel. bias
✓
✓
✓
✗
1.05
38.40
0.110
96.20
4.88
0.08
0.06
0.18
0.14
0.20
+ Global context (Ours)
✓
✓
✓
✓
0.94
39.03
0.094
98.10
4.69
0.07
0.06
0.13
0.11
0.15
Appendix
Table 10: Ablation of relation-aware components in edge-gated relational DiT (Waymo). We incrementally add relational modules to the factorized DiT backbone. Relational bias is critical for graph connectivity (Conn/Reach). Cross-type bias improves agent–lane geometric consistency (e.g., Ang. JSD) under the same map. Relational bias and value gating improve structural validity (e.g., route validity and endpoint distance) under large-step sampling. Our full model achieves the best structural integrity and safety.
Training recipe
Key design
Train GPU-h ↓
Steps at test
Waymo (same decoder)
MeanFlow ( uθ )
JVP ( ∂tu )
Two-time ( t,Δ )
Distill ( 1-step )
EPD (m) ↓
Agent JSD ↓
Time (ms) ↓
Valid (%) ↑
Flow matching
✗
✗
✗
✗
320
1-step
8.520
4.250
5.6
9.3
✗
✗
✗
✗
320
12-step
0.150
0.120
31.0
95.0
MeanFlow (Identity)
✓
✗
✗
✗
300
1-step
0.554
0.499
5.6
63.2
✓
✗
✗
✗
300
12-step
0.120
0.110
31.0
96.5
MeanFlow (Id + JVP)
✓
✓
✗
✗
400
1-step
0.293
0.312
5.6
68.0
Appendix
Table 11: Impact of the meanflow ( Geng et al., 2025 ) objective on solver-free sampling. We compare different training objectives under a fixed step budget. Training Cost is measured in GPU hours on 8 × H20. Standard Flow Matching (FM) fails completely at 1-step (EPD 8.52m). Distillation is fast but blurs details (High Agent JSD). Our MeanFlow (JVP+2-time) incurs higher training cost (+50%) but enables the only viable 1-step generation (EPD 0.269m) that preserves agent statistics (JSD 0.136), enabling real-time streaming.
Dynamics
Sampler / steps
Waymo
nuPlan
EPD (m) ↓
Agent JSD ↓
Time (ms) ↓
EPD (m) ↓
Agent JSD ↓
Time (ms) ↓
Flow (Rectified)
Flow-12
0.150
0.120
28
0.125
0.155
31
Flow-24
0.110
0.105
55
0.095
0.140
55
Flow-32
0.098
0.091
73
0.088
0.135
73
Flow-48
0.089
0.084
110
0.082
0.130
110
MeanFlow
MeanFlow-1
0.269
0.136
5.6
0.224
0.171
6
Appendix
Table 12: Step-budget sensitivity of our latent generator (numeric companion). Detailed metrics for Figure 6 . While DDPM (100 steps) achieves the lowest EPD (Waymo: 0.080m; nuPlan: 0.072m), its latency (158ms) is the highest and limits online use. Our MeanFlow-5 provides a favorable balance between fidelity and latency, while MeanFlow-1 enables ultra-low latency streaming.
Method
Design toggles
Open-loop
Closed-loop feasibility (%) ↓
Efficiency
RTG (1-pass)
Hybrid A+R
Logit shaping
DKAL loss
ADE (m) ↓
ρ↑
Coll.
Yaw rate
Lat. acc.
Lon. jerk
Lat. (ms) ↓
Fwd ↓
Ctrl-Sim ( Rowe et al., 2024 )
✗
✗
✗
✗
2.80
-0.25
15.2
8.5
14.2
10.5
36.9
2.0
Δ Sim (discrete-only)
✓
✗
✓
✓
2.62
0.39
8.5
4.2
5.5
6.2
21.7
1.0
Δ Sim (hybrid A+R, no DKAL)
✓
✓
✓
✗
2.10
0.24
10.1
6.8
12.5
8.9
26.1
1.0
Δ Sim (hybrid A+R, no shaping)
✓
✓
✗
✓
1.95
0.45
5.2
2.5
3.1
4.5
26.1
1.0
Δ Sim (Ours)
✓
✓
✓
✓
1.72
0.53
2.9
1.2
2.1
3.2
26.1
1.0
Appendix
Table 13: Δ Sim component analysis on accuracy, controllability, and feasibility (Waymo). We evaluate the impact of Hybrid Action Head (A+R) and Differentiable Kinematic Alignment Loss (DKAL). Ctrl-Sim baseline suffers from poor controllability ( ρ=−0.25 ) and high latency. Our full Δ Sim achieves the lowest ADE (1.72m) and highest controllability ( ρ=0.53 ). Crucially, DKAL significantly reduces closed-loop physical violations (e.g., Lat. Acc. 12.5% → 2.1%), ensuring stable long-horizon rollouts.
Panel A: Fixed-horizon cross-backend evaluation (200 m).
Policy
Train backend
Train data
Train GPU-h
Eval: Log Replay
Eval: ScenDream-L (neg.)
Eval: VectorWorld (neg.)
(#eps)
C/O/Succ (%)
Time (h)
C/O/Succ (%)
Time (h)
C/O/Succ (%)
Time (h)
PPO
Waymo Log
100k
64
29.3 / 6.9 / 63.8
0.4
59.0 / 9.0 / 32.1
5.8
65.5 / 9.5 / 25.0
1.2
PPO
ScenDream-L
100k
480
19.3 / 5.9 / 74.8
0.4
45.2 / 8.5 / 46.3
5.8
40.9 / 7.6 / 48.5
1.2
PPO
VectorWorld
100k
160
18.1 / 6.2 / 75.7
0.4
38.5 / 5.6 / 56.3
5.8
27.1 / 5.0 / 66.9
1.2
Panel B: Long-horizon evaluation (1 km + ; VectorWorld only).
Appendix
Table 14: Policy training value with cross-backend evaluation (Waymo). To reduce the risk of simulator overfitting, we evaluate policies across different backends under matched horizons. A policy retrained in VectorWorld improves success not only in VectorWorld but also transfers to log replay and ScenDream backends (see Panel A). Panel B further evaluates long-horizon performance ( 1km+ ) in VectorWorld.
Source of failures
Matching and reproduction diagnostics
Outcome agreement
#Fail episodes
Log match (%)
Init. state dist. (L2) ↓
Route match (%)
Fail repro. (%)
Type agreement (%)
Log replay (reference)
100
100.0
0.00
100.0
100.0
100.0
ScenDream-L (neg. tilt)
528
65.2
1.42
82.5
45.2
52.1
VectorWorld (neg. tilt)
655
88.5
0.92
95.4
72.0
78.5
Appendix
Table 15: Failure reproduction across backends. We verify if failures discovered in simulation correspond to realistic crash types. We match generated failure scenarios to the nearest log scenarios based on map and agent topology. VectorWorld failures show high Type Agreement (78.5%) with log data, indicating that our simulator exposes realistic safety-critical events rather than simulation artifacts.
Figure 8: Waymo qualitative comparison for initial scene generation (64m × 64m). We compare VectorWorld against representative vectorized scene generators and the Waymo reference. The visualization highlights lane connectivity at intersections, agent–lane geometric consistency, and the plausibility of the initialized interaction state (including short motion history when available).
Figure 9: nuPlan qualitative comparison with traffic-light semantics. Lane centerlines are colored by traffic-light state (green vs. red) to visualize control-relevant map semantics. We compare VectorWorld with strong baselines under the same vectorized rendering.
Figure 10: Agent controllability under fixed map conditioning. The map (lane graph) is held fixed as a condition, while the agent configuration is generated under different controllability settings. This visualization isolates controllability from map diversity by using the same conditioned lanes across all panels.
Figure 11: End-to-end generation latency (timeline view). Qualitative snapshots under increasing time budgets for a 64m×64m tile. VectorWorld reaches the final lane–agent vector scene with one solver-free MeanFlow step plus one VAE decode ( ≈6 ms), whereas multi-step diffusion baselines only converge at substantially higher budgets (e.g., ∼160 ms).
Figure 12: End-to-end generation latency. A different scene instance rendered with the same timing protocol (latent sampling + one VAE decode). The result is consistent: VectorWorld completes a full 64m×64m lane–agent tile in ≈6 ms via a single MeanFlow update, while solver-based diffusion requires many iterative denoising calls.
Figure 13: Planner-relevant challenging scenarios sampled from VectorWorld. We render a subset of VectorWorld-generated scenes using the protocol in Section A.15 . These scenarios illustrate diverse intersection geometries, dense multi-agent interactions, and tight gaps that are valuable for stress testing and training an ego PPO planner in closed loop.
Figure 14: Streaming outpainting in closed-loop rollout (case study 1). The simulator repeatedly outpaints new lane–agent tiles near the frontier while clamping the observed region. The visualization highlights seam consistency and stable long-horizon progression.
Figure 15: Streaming outpainting with dynamic agent set and per-agent intent control (case study 2). The visualization illustrates stable long-horizon expansion with agent insertion/removal and controllable behaviors, enabled by the interaction-state interface .