To Route or to Adapt? Multi-Expert Diffusion Planners in Unseen Regions

Yun Li; Ehsan Javanmardi; Simon Thompson; Jiachen Gong; Qunli Zhang; Zifan Zeng; Shiming Liu; Peng Wang

cs.ROOct 22, 2026

To Route or to Adapt? Multi-Expert Diffusion Planners in Unseen Regions

Authors: Yun Li, Ehsan Javanmardi, Simon Thompson, Jiachen Gong, Qunli Zhang, Zifan Zeng, Shiming Liu, Peng Wang,

Organizations: The University of Tokyo · TIER IV, Inc. · Huawei

Abstract

Diffusion trajectory planners with domain-specific experts face a practical question in unseen regions: can they rely on selecting among existing experts, or must the planner itself adapt? We study this question using a planner with a shared adapter and per-domain expert adapters. Across three real-world held-out maps, none of eight test-time routing schemes improves the fleet-mean lateral offset over the static default, which uses the same expert for every scene. Even an oracle that selects the best expert for each scene reduces the mean offset by only 0.9 m. In contrast, reward-based fine-tuning on just 20 target-region scenes yields substantially larger gains. On matched evaluation slices, joint replay achieves a fleet-mean offset of 6.9 m, compared with 12.4 m for the static default. Comparisons under the same target-region training budget show that target-region training drives the improvement, while replaying training scenes limits forgetting on the original ODDs. On nuPlan, fine-tuning across training cities also improves open-loop offsets, although closed-loop performance deteriorates. Further diagnostics reveal that two test-time adaptation baselines achieve low offsets by producing degenerate trajectories. These results show the limited headroom for selecting among existing experts and the greater open-loop gains available from adapting the planner.

Figures & tables

Figure 1: Method overview aligned with the Autoware E2E Generator–Selector reference architecture [ 3 ] . The Generator (the adapter stack) emits $K{=}4$ candidate trajectories, and the Selector chooses one by routing or scoring; the vMF mixture and the fine-tune mechanisms of § 5 instead change the Generator’s weights; a Safety Gate enforces the Reachability-of-Safe-State constraint.

Experiment	Model evaluated	Training	Evaluation
Routing schemes (§ 4 )	adapter stack	selector only	Pool A ( $24$ )
Oracle headroom (§ 4 )	per-scene oracle	none	Pool A; $104$ scenes
vMF mixture (§ 5.1 )	average of experts	closed-form weights	Pool A ( $24$ )
Shared-adapter repair (§ 5.2 )	shared module	$500$ steps, perturbed scenes	Pool A ( $24$ )
Joint replay, baselines (§ 5.3 )	adapter stack	$500$ steps, $20$ target scenes	Pool B, $8$ seeds
nuPlan cross-city (§ 6 )	rank- $4$ shared LoRA	$500$ steps on $3$ cities	nuPlan, open loop

Table 1: Model, training and evaluation pool of each experiment (pools defined in § 3 ).

Figure 2: Three constructive mechanisms. (A) vMF mixture: experts weighted by distance to the deployment location (§ 5.1 ). (B) Shared-adapter repair: only the shared module is fine-tuned, on perturbed training scenes (§ 5.2 ). (C) Joint replay: the whole adapter stack is fine-tuned on training and target-region scenes; inset: target-region error (§ 5.3 ).

Routing scheme	Knowledge Hub		Ishiodai		Morikoro		Fleet
Scene-conditioned MLP	4.5	$\pm$ 0.8	9.0	$\pm$ 4.2	63.3	$\pm$ 58.0	25.61
Self-consistency	14.3	$\pm$ 4.1	7.7	$\pm$ 4.6	46.3	$\pm$ 35.3	22.76
Self-consistency (normalised)	14.3	$\pm$ 4.1	7.7	$\pm$ 4.6	46.3	$\pm$ 35.3	22.76
Lane-following	6.0	$\pm$ 2.1	7.8	$\pm$ 4.0	41.1	$\pm$ 46.9	18.29
Denoising-loss	14.0	$\pm$ 4.0	8.1	$\pm$ 4.3	42.9	$\pm$ 33.7	21.67
Conformal corridor ( $T{=}15$ )	4.0	$\pm$ 0.1	4.6	$\pm$ 0.7	38.9	$\pm$ 37.1	15.86

Table 2: Eight routing schemes versus the static default: lateral offset (m) on Pool A, mean

\pm

std over scenes, and the fleet mean. Six of the eight are significantly worse than the default under paired per-scene tests (

p\leq 0.012

), none significantly better. The reward-supervised gate was run on Morikoro only (

\pm

over

50

seeds).

Figure 3: (a) Lateral offset of the routing schemes (gray) and the static default (blue) on each held-out map; two schemes are omitted because the normalised self-consistency equals the vanilla one and the reward-supervised gate ran on Morikoro only. (b) Fleet mean of the three constructive mechanisms and its change relative to the shared module only. Pool A; joint replay excludes its

7

Ishiodai training scenes.

Appendix figures & tables40 assets

Supplementary material from the paper’s appendix.

Appendix

Main text	Appendix	Page	Content
§ 3	L	L	Hyperparameters, training recipes, train/eval split tooling
§ 4	Q	Q	Held-out target-region topologies
	M	M	Why each routing scheme fails; oracle details
	K	K	Routing feature ablations
	N	N	Conformal calibration
	R	R	Regions where the nearest expert is not ODD-Nagoya (also § 7 )

Appendix

Table 4: Guide to the appendix, ordered by the main-text section each part supports.

Method	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Shared module only (TTA slice)	$14.26\pm 4.13$	$7.43\pm 6.11$	$37.40\pm 29.68$	$19.70$
Shared module only (HyperLN slice)	—	—	—	$22.76$
TENT-LN ( $K{=}4$ , $5$ steps)	$14.15\pm 4.18$	$7.47\pm 6.14$	$36.99\pm 29.45$	$19.54$
TENT-online ( $K{=}32$ , epoch $1$ )	—	—	—	$\mathbf{4.11}$
TENT-online ( $K{=}32$ , epoch $10$ )	—	—	—	$5.09$
TENT-online SAR ( $K{=}32$ , epoch $4$ )	—	—	—	$4.56$

Appendix

Table 5: Test-time adaptation baselines on the disjoint target-region evaluation pool of seed

7

. TENT updates only the affine parameters of the decoder LayerNorm layers, using a trajectory-variance loss over

K

samples. TENT-LN:

K{=}4

5

SGD steps, fresh model for each scene. TENT-online:

K{=}32

, Adam with lr

=10^{-3}

10

epochs, model state carried over between scenes.

Recipe	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Shared module only	$14.26$	$7.72$	$46.30$	$22.76$
Static default (ODD-Nagoya)	$4.51$	$4.82$	$31.88$	$13.74$
Joint replay (single checkpoint)	$2.24$	$2.77$	$7.78$	$4.26$
HyperLN, $h{=}64$ , no jitter (best single seed)	$11.19$	$1.34$	$4.68$	$5.74$
HyperLN, $h{=}64$ , no jitter, $3$ -seed mean	$12.17\pm 1.18$	$1.39\pm 0.20$	$5.26\pm 0.39$	$6.27\pm 0.59$
HyperLN, $h{=}16$ , jitter $0.1^{\circ}$ (capacity ablation)	$15.42$	$1.95$	$15.71$	$11.02$

Appendix

Table 6: Lateral offset of hypernetwork-conditioned LayerNorm before the diagnostic probe of Table 7 .

Configuration	lat (m)	progress (m, 8 s)	speed (m/s)	cross-scene $L_{2}$
Frozen shared module only	$24.89$	$170.0$	$21.3$	$150.4$
Static default (ODD-Nagoya)	$16.04$	$166.7$	$20.8$	$105.0$
vMF mixture $\tau{=}200$ km	$19.64$	$172.2$	$21.5$	$124.2$
Hypernet-LN (this work)	$5.27$	$\mathbf{12.3}$	$\mathbf{1.5}$	$73.0$
Hypernet-LN $+$ TENT polish	$1.21$	$\mathbf{3.7}$	$\mathbf{0.46}$	$\mathbf{1.2}$
Static default $+$ TENT polish	$3.40$	$174.8$	$21.9$	$\mathbf{10.2}$

Appendix

Table 7: Diagnostic probe of the hypernetwork-LN recipe (§ B.1 ) and of the TENT polish variants (§ A.1 ). Forward progress is

\|x(T)-x(0)\|

T{=}8

s; mean speed is progress

/T

. Cross-scene

L_{2}

is the mean pairwise distance between the trajectories of different scenes, each centred at its own starting frame; healthy models give a large

L_{2}

$\tau$	$\alpha$ (Hongo, Kashiwa, Shalun, Nagoya)	Knowledge Hub	Ishiodai	Morikoro
$\to 0$ (hard MAP $=$ ODD-Nagoya)	$(0,\,0,\,0,\,1)$	$4.51$	$4.82$	$31.9$
$200$ km (soft mix, headline)	$(0.20,\,0.18,\,0.00,\,0.62)$	$4.02$	$4.63$	$38.9$
$\to\infty$ (uniform soup)	$(0.25,\,0.25,\,0.25,\,0.25)$	—	—	—

Appendix

Table 8: vMF mixture weights

\alpha

and per-map lateral offset (m) across

\tau

Distance metric	$\alpha_{\text{Hongo}}$	$\alpha_{\text{Kashiwa}}$	$\alpha_{\text{Shalun}}$	$\alpha_{\text{Nagoya}}$
Haversine (great-circle)	$0.1981$	$0.1774$	$0.0000$	$0.6245$
ECEF chord on $S^{2}$	$0.1982$	$0.1774$	$0.0000$	$0.6244$
Equirectangular flat-Earth	$0.1981$	$0.1774$	$0.0000$	$0.6245$
Local-tangent-plane (UTM)	$0.1981$	$0.1774$	$0.0000$	$0.6245$

Appendix

Table 9: Mixing weights

\alpha

of the vMF mixture for Morikoro at

\tau{=}200

km under four distance metrics.

$\tau$ (km)	Knowledge Hub	Ishiodai	Morikoro
$1$ / $10$ / $50$ (one-hot $\to$ static default)	$4.51\pm 0.79$	$4.82\pm 0.84$	$\mathbf{31.9\pm 32.1}$
$200$ (soft mix)	$\mathbf{4.02\pm 0.11}$	$4.63\pm 0.68$	$38.9\pm 37.1$
$200$ (top-2 mix)	$4.13\pm 0.73$	$\mathbf{4.49\pm 0.80}$	$40.7\pm 37.7$

Appendix

Table 10: Lateral offset (m) of the vMF mixture at four temperatures. As

\tau{\to}0

the mixture reduces to the static default (all weight on ODD-Nagoya); as

\tau{\to}\infty

it becomes the uniform average of the experts.

Configuration	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
ODD-Hongo (ODD-Hongo) alone	$5.99$	$39.06$	$55.59$	$33.55$
ODD-Kashiwa (ODD-Kashiwa) alone	$5.98$	$31.52$	$22.90$	$20.13$
ODD-Shalun (ODD-Shalun) alone	$13.6$	$31.53$	$30.63$	$25.25$
ODD-Nagoya (ODD-Nagoya) alone	$\mathbf{4.51}$	$\mathbf{31.58}$	$\mathbf{17.48}$	$\mathbf{17.86}$
Soup {D, B} (trial)	$4.62$	$31.80$	$19.93$	$18.78$
Soup {D, C} (trial)	$4.79$	$29.90$	$22.30$	$19.00$

Appendix

Table 11: Greedy soup of the four per-ODD experts on the seed-

7

disjoint target-region evaluation pool (CRC32 split, App. L ). The experts are ranked by fleet mean (lowest first), the soup is initialised with the best one, and each subsequent expert is added only if the uniformly averaged soup improves on the evaluation pool. In the trial rows, A, B, C and D denote ODD-Hongo, ODD-Kashiwa, ODD-Shalun and ODD-Nagoya. Reference rows give the uniform soup over all four experts and the vMF mixture at

\tau{=}200

km (GPS soft mix); the latter is copied from Table 10 , was measured on Pool A, and is not comparable with the other rows.

Figure 5: Two-dimensional slice of the loss/error landscape spanned by two per-ODD experts, drawn in the style of Figure 2 of Wortsman et al. [ 13 ] . The anchors are

\theta_{0}

(shared module only; fleet mean

20.11

m, Morikoro

39.67

m),

\theta_{1}

(ODD-Nagoya;

19.41

34.94

\theta_{2}

(ODD-Kashiwa;

22.96

41.16

) and

\theta_{\mathrm{soup}}{=}\tfrac{1}{2}(\theta_{1}+\theta_{2})

(

20.70

37.64

). Only these four points are evaluated; the surface is a thin-plate-spline interpolation through them.

Soup	Knowledge Hub	Ishiodai	Morikoro	Fleet
$\{$ ODD-Nagoya, ODD-Kashiwa $\}$	$+0.63$	$-0.26$	$+0.26$	$+0.21$
$\{$ ODD-Nagoya, ODD-Shalun $\}$	$+4.27$	$+1.66$	$+1.76$	$+2.56$
$\{$ ODD-Nagoya, ODD-Hongo $\}$	$+1.46$	$+1.20$	$+5.45$	$+2.70$
Uniform $\{$ D, B, C, A $\}$	$+2.60$	$+0.51$	$+4.06$	$+2.39$

Appendix

Table 12: Interpolation advantage

\Delta_{\mathrm{I}}

(mean endpoint error minus soup error) for each two-expert and four-expert uniform soup on the seed-

7

CRC32-disjoint target-region evaluation pool (App. L ). Positive values indicate that the soup beats the arithmetic mean of its endpoints, a bonus from linear mode connectivity. Table 13 reports

\Delta_{\mathrm{gap}}

for the same rows.

Soup	Knowledge Hub	Ishiodai	Morikoro	Fleet
$\{$ ODD-Nagoya, ODD-Kashiwa $\}$	$+0.10$	$+0.29$	$+2.45$	$+0.93$
$\{$ ODD-Nagoya, ODD-Shalun $\}$	$+0.28$	$\mathbf{-1.63}$	$+4.82$	$+1.14$
$\{$ ODD-Nagoya, ODD-Hongo $\}$	$\mathbf{-0.72}$	$+2.54$	$+13.61$	$+5.14$
Uniform $\{$ D, B, C, A $\}$	$+0.41$	$+1.39$	$+10.11$	$+3.95$

Appendix

Table 13: Gap to the best endpoint,

\Delta_{\mathrm{gap}}

(soup error minus the error of the best single endpoint; positive values mean the soup is worse), for the same soups as Table 12 on the seed-

7

CRC32-disjoint target-region evaluation pool (App. L ). Bold cells have negative

\Delta_{\mathrm{gap}}

: the soup beats the best single expert, the strict soup effect of Wortsman et al.

Configuration	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Best single (ODD-Nagoya, Table 11 )	$\mathbf{4.51}$	$\mathbf{31.58}$	$\mathbf{17.48}$	$\mathbf{17.86}$
Uniform soup all 4 (Table 11 )	$4.93$	$32.91$	$27.60$	$21.81$
TIES-Merging, keep-density $20\%$ (canonical Yadav)	$5.83$	$35.56$	$26.14$	$22.51$
TIES-Merging, keep-density $50\%$ (ablation)	$5.19$	$35.05$	$26.88$	$22.37$
Uniform soup all 4 (TIES re-eval, cuDNN noise)	$6.07$	$32.30$	$28.51$	$22.29$
Joint-replay from-scratch (the rank-allocation sweep) – reference	$1.94$	$6.00$	$6.81$	$\mathbf{4.92}$

Appendix

Table 14: TIES-Merging [ 14 ] of the four per-ODD experts at two keep-densities, evaluated on the seed-

7

CRC32-disjoint target-region evaluation pool (App. L ). Reference rows are taken from Table 11 and from the joint-replay frontier of § 5.3 .

Configuration	Knowledge Hub	Ishiodai	Morikoro
Static default (ODD-Nagoya) (original shared)	$4.51\pm 0.79$	$4.82\pm 0.84$	$31.88\pm 32.05$
shared module only, original	$14.3\pm 4.1$	$7.7\pm 4.6$	$46.3\pm 35.3$
shared module only, repaired	$6.0\pm 2.2$	$6.1\pm 1.6$	$\mathbf{21.4\pm 26.0}$
ODD-Hongo + repaired-shared	$24.5\pm 13.2$	$17.6\pm 6.4$	$50.3\pm 43.2$
ODD-Kashiwa + repaired-shared	$7.9\pm 0.5$	$7.8\pm 0.5$	$\mathbf{11.1\pm 10.5}$
ODD-Shalun + repaired-shared	$6.0\pm 2.1$	$5.8\pm 1.5$	$18.3\pm 24.9$

Appendix

Table 15: Per-expert lateral offset (m) on the three held-out maps before and after fine-tuning the shared module on procedurally perturbed training-ODD scenes.

Configuration	Knowledge Hub (seeds)	Ishiodai (seeds)	Morikoro (seeds)	Morikoro per-seed
Baseline: rot + bezier + drop	$\mathbf{5.99\pm 2.23}$	$\mathbf{6.05\pm 1.63}$	$\mathbf{21.4\pm 26.0}$	single seed
$-$ SE(2) rotation	$6.05\pm 3.37$	$7.12\pm 3.61$	$33.13\pm 7.24$	$[41.4,28.0,29.9]$
$-$ Bezier curvature warp	$7.01\pm 2.99$	$7.53\pm 2.69$	$26.28\pm 4.70$	$[31.5,22.4,24.9]$
$-$ Boundary drop	$6.95\pm 2.50$	$7.56\pm 2.19$	$28.12\pm 13.96$	$[44.1,22.0,18.3]$

Appendix

Table 16: Ablation of the perturbation components used for shared-module repair, with three independent seeds per ablation row; the baseline row is a single seed. Each ablation row repeats the same

500

-step fine-tune of the shared module with one perturbation component disabled.

Map	Max lateral (m)	Forward progress (m)	Static default (m)	Change
Knowledge Hub	$18.63\pm 6.19$	$156.80\pm 2.34$	$4.51$	$+313\%$
Ishiodai	$19.32\pm 30.53$	$149.61\pm 25.40$	$31.58$	$-39\%$
Morikoro	$37.83\pm 20.69$	$151.00\pm 14.18$	$17.48$	$+116\%$

Appendix

Table 17: Distilled regional adapter on the three held-out maps, with training and evaluation scenes drawn from disjoint lanelets (§ 3 ). Each cell gives the mean and standard deviation over the seed-

7

evaluation pool of road lanelets. The adapter is a single

78

K-parameter rank-

4

LoRA on the base planner, with no per-ODD modules.

Figure 6: Pareto view of target-region offset against forgetting for the weight-space baselines and the joint-replay configurations. Horizontal axis: regression on the training ODDs, measured as the increase in route deviation summed over the four training ODDs (

\Delta{=}0

is the frozen adapter stack). Vertical axis: target-region fleet-mean lateral offset on the CRC32-disjoint seed-

7

pool. Step line: empirical Pareto frontier. Star: the from-scratch

r{=}4

checkpoint at

(+13.30,7.35)

, which has not been deployed on the vehicle.

$n_{\mathrm{target-region}}$	fleet (seed- $42$ , m)	fleet (3-seed mean $\pm$ std, m)	Training-ODD $\sum\!\Delta_{\mathrm{route\_dev}}$ (m)	Training-ODD $\sum\!\Delta_{\mathrm{progress}}$ (m)	Train wall-clock
Pre (shared module only; $n_{\mathrm{train}}{=}80$ eval slice)	$17.48$	—	—	—	—
$\phantom{0}5$	$6.76$	$\phantom{0}9.79\pm 5.14$	$+5.00$	$+25.86$	$4.5$ min
$10$	$7.54$	$10.14\pm 6.62$	$\mathbf{-0.33}$	$+3.29$	$4.5$ min
$20$	$5.51$	$\phantom{0}6.17\pm\mathbf{1.23}$	$+2.43$	$+21.37$	$4.5$ min
$40$	$5.10$	$\phantom{0}5.67\pm\mathbf{1.06}$	$+0.54$	$+4.69$	$4.4$ min
$80^{\dagger}$	$\mathbf{4.44}$	— ( $\dagger$ )	$+0.23$	$-0.56$	$4.3$ min

Appendix

Table 18: Sample complexity of joint replay with the inherited shared module (inherit-shared) on CRC32-disjoint seed-

7

target-region evaluation slices (

24

scenes per training seed, drawn from the lanelets left after that seed’s training selection; see App. L ). Each row is a separate joint-replay training run with the given target-region pool size, a training-ODD to target-region ratio of

10

1

, and

500

optimiser steps. Column 2: fleet mean for a single seed (seed-

42

). Column 3: fleet mean over seeds

\{42,43,44\}

, each scored on its own evaluation slice; the

n{=}80

row has a single seed and is marked

\dagger

. The training-ODD columns sum over the four training ODDs.

Configuration	Knowledge Hub	Ishiodai	Morikoro
Static default (no adaptation)	$\mathbf{4.51}$	$4.82$	$31.88$
Distilled regional adapter ( $78$ K params, $1.5$ min)	$6.10$	$\mathbf{4.05}$	$\mathbf{18.88}$
Skyline rank- $128$ LoRA ( $2.5$ M params, $\approx 15$ min)	$24.09\pm 0.02$	$24.28\pm 0.09$	$24.35\pm 0.12$

Appendix

Table 19: Skyline, an upper bound overfit to the held-out scenes, versus the deployable distilled adapter. Skyline:

2.5

M-parameter rank-

128

LoRA trained for

2000

optimiser steps; distilled adapter:

78

K-parameter rank-

4

LoRA,

300

optimiser steps,

1.5

min.

Configuration	Boston eval	Pittsburgh eval	Las Vegas eval	Singapore eval
Base (single seed)	$2.17$	$4.51$	$1.86$	$8.64$
Boston held-out (3 seeds)	$\mathbf{1.63\pm 0.16}$	$3.15\pm 0.24$	$1.25\pm 0.20$	$5.10\pm 0.30$
Pittsburgh held-out (3 seeds)	$1.71\pm 0.21$	$\mathbf{3.40\pm 0.37}$	$1.37\pm 0.27$	$5.61\pm 0.66$
Las Vegas held-out (3 seeds)	$1.71\pm 0.18$	$3.27\pm 0.21$	$\mathbf{1.34\pm 0.18}$	$5.44\pm 0.46$
Singapore held-out (3 seeds, LHT)	$1.71\pm 0.25$	$3.49\pm 0.44$	$1.42\pm 0.27$	$\mathbf{5.60\pm 0.78}$

Appendix

Table 20: nuPlan

4{\times}4

leave-one-city-out transfer matrix over three seeds. For each held-out city (row), a 3-city LoRA is trained on the other three cities with three independent seeds; each cell gives the mean

\pm

std over seeds on one of the four cities (columns). Held-out diagonal entries are in bold. The base row (single seed) is the nuPlan BC checkpoint evaluated on the same fixed pool.

LoRA training set	Boston	Pittsburgh	Las Vegas	Singapore
None (base BC)	$2.14\pm 6.68$	$4.58\pm 8.92$	$1.80\pm 3.95$	$8.55\pm 10.09$
3-city, holdout Boston	$[1.71\pm 4.55]$	$\mathbf{3.03\pm 5.94}$	$1.36\pm 2.50$	$5.40\pm 6.53$
3-city, holdout Pittsburgh	$1.71\pm 4.24$	$[3.50\pm 6.42]$	$\mathbf{1.34\pm 2.21}$	$5.41\pm 6.51$
3-city, holdout Las Vegas	$\mathbf{1.62\pm 4.28}$	$3.36\pm 6.48$	$[1.25\pm 2.31]$	$\mathbf{5.30\pm 6.46}$
3-city, holdout Singapore	$2.05\pm 4.42$	$3.69\pm 6.37$	$1.86\pm 2.77$	$[5.93\pm 6.68]$

Appendix

Table 21: nuPlan

4{\times}4

cross-city transfer matrix. Each row is a LoRA trained on three cities and evaluated on all four; the held-out city is shown in [brackets]. Maximum lateral offset (m),

50

scenes per city.

Recipe	Trainable params	LR	Steps	Wall-clock
Shared-module repair (§ 5.2 )	$78{,}368$	$5\!\times\!10^{-5}$	$500$	$3.9$ min
Rank- $8$ shared replication (App. E )	$156{,}736$	$5\!\times\!10^{-5}$	$500$	$4.0$ min
Regional-adapter distillation (§ F.1 )	$78{,}368$	$1\!\times\!10^{-4}$	$300$	$1.5$ min
Joint replay (§ 7 )	$862{,}048$	$5\!\times\!10^{-5}$	$500$	$5.0$ min
Joint-replay sample-complexity (§ H.1 )	$862{,}048$	$5\!\times\!10^{-5}$	$500$	$4.4{-}5.7$ min each
Skyline rank- $128$ (§ I.1 )	$\sim\!2.5\!\times\!10^{6}$	$5\!\times\!10^{-5}$	$2000$	$15$ min

Appendix

Table 22: Hyperparameters of the training recipes: optimisation budget. The budgets exclude the training of the underlying base planner, which is not part of this paper’s contribution. The loss and training data of each recipe are given in Table 23 .

Recipe	Loss	Train data
Shared-module repair (§ 5.2 )	ODD reward	$4{\times}50$ training-ODD npz, perturbed in-place
Rank- $8$ shared replication (App. E )	ODD reward	same as above
Regional-adapter distillation (§ F.1 )	MSE to teacher trajectory	$60$ seed- $42$ target-region train scenes
Joint replay (§ 7 )	ODD reward	$200$ prod npz + $20$ target-region seed- $42$
Joint-replay sample-complexity (§ H.1 )	ODD reward	$200$ prod + $\{5,10,20,40,80\}$ target-region
Skyline rank- $128$ (§ I.1 )	ODD reward	$24$ target-region eval scenes (overfit)

Appendix

Table 23: Hyperparameters of the training recipes: loss and training data (companion to Table 22 ). In the training-data column, “npz” denotes scene files and “prod” denotes the training ODDs.

Component	Parameters	Role
Base Diffusion-Planner (vanilla, no LoRA)
encoder (frozen)	$7{,}419{,}264$	frozen
decoder (frozen)	$7{,}083{,}929$	frozen
of which DiT total	$7{,}082{,}564$	frozen
DiT.preproj (fc1 $+$ fc2)	$\phantom{0,0}297{,}728$	LoRA target
DiT.blocks ( $\times 3$ )	$5{,}922{,}816$	mixed

Appendix

Table 24: Parameter counts of the Diffusion-Planner base planner and of the adapter stack applied on top of it. Only the linear layers of the DiT MLPs are LoRA-wrapped; the attention and normalisation blocks stay frozen and are not modulated.

			Calibration residual (m)		$q_{e}$ (m)
Expert	$n_{\mathrm{train}}$	$n_{\mathrm{cal}}$	mean	std	split-conformal	in-sample
ODD-Hongo	$108$	$12$	$20.5$	$20.0$	$67.9$	$83.5$
ODD-Kashiwa	$108$	$12$	$17.4$	$11.0$	$34.2$	$53.9$
ODD-Shalun	$108$	$12$	$11.4$	$4.6$	$17.1$	$15.5$
ODD-Nagoya	$108$	$12$	$32.6$	$20.4$	$61.4$	$33.4$

Appendix

Table 25: Split-conformal calibration of each expert. For calibration,

40\%

of each expert’s own-ODD scenes are held out (

n{=}12

), and the split-conformal

q_{e}

uses the finite-sample order statistic

\lceil(1-\alpha)(n{+}1)\rceil/n

\alpha{=}0.1

. The last column reports the in-sample residual quantile, which has no coverage interpretation.

Rank	Model	strict %	drv %	cmf %
1	DPO+L2+SAM (this work, headline)	$0.00$	$100.0$	$\mathbf{0.00}$
1	DPO+L2+SAM (block-restricted, LoRA on blocks.0..2 only)	$0.00$	$99.8$	$\mathbf{0.00}$
1	greedy soup (degenerate; $\to$ sam alone)	$0.00$	$100.0$	$\mathbf{0.00}$
4	Base (no LoRA, Plan-R1 base planner)	$0.00$	$97.2$	$0.80$
5	DPO+L2 ( $w_{\mathrm{imit}}{=}0.9$ )	$0.00$	$100.0$	$3.80$
6	DPO+L2 ( $\beta_{\mathrm{DPO}}{=}0.01$ )	$0.00$	$100.0$	$5.00$

Appendix

Table 26: Final comparison (Phase 4) on

n{=}500

ODD-Kashiwa validation scenes, disjoint from the training scenes, scored with the V3 proxy (§ O.1 ). Each entry is the percentage of the

500

scenes in which at least one criterion of the layer is triggered ( any_triggered ). strict : hard-constraint layer; drv : careful-and-competent driver layer; cmf : comfort layer.

Figure 7: Strict-safety and comfort-violation rates in the final comparison (Phase 4) on

n{=}500

ODD-Kashiwa validation scenes, disjoint from the training scenes, under V3 (§ O.1 ). The comfort layer combines the jerk , lat_acc and speed_change criteria. Rows match the model rows of Table 26 ; only the last model has strict-safety violations.

Figure 8: Per-layer ablation of the Reward-back-prop LoRA. Each of the 16 LoRA-adapted DiT layers is zeroed in turn, and the comfort-violation rate is measured on

n{=}30

held-out scenes.

Figure 9: The test vehicle and its chassis specifications, as listed by the manufacturer.

Bag	$n$	strict %	drv %	cmf %	Note
rep1 baseline	$27154$	$0.1$	$2.1$	$\mathbf{37.7}$	human driver
rep1 (ODD-Kashiwa adapter)	$14275$	$0.8$	$5.2$	$\mathbf{47.7}$	adapter, autonomous
rep2 (ODD-Kashiwa adapter)	$15755$	$0.0$	$0.0$	$\mathbf{0.0}$	crept $72$ m, then stopped

Appendix

Table 27: V3 scores of ego trajectories recorded on the real vehicle. rep1 baseline: a human driver drives a loop of the ODD-Kashiwa course. rep1 (ODD-Kashiwa adapter): the planner, with the reward-trained shared-plus-expert adapter and the ODD-Kashiwa expert, drives the same course autonomously on the same day. rep2 (ODD-Kashiwa adapter): a second autonomous run on the same day, in which the vehicle crept

72

m and then stopped without recovering.

Model	Origin	strict %	cmf %	Real vehicle
DPO+L2+SAM (proposed)	this work	$0.00$	$\mathbf{0.00}$	simulation only
DPO+L2+SAM (block-restricted)	this work	$0.00$	$0.00$	simulation only
Production DPO (human labels)	production, $3$ months	$0.00$	$\mathbf{0.40}$	validated (April)
Base (no LoRA)	Plan-R1 base planner	$0.00$	$0.80$	simulation only
Reward-back-prop	reward-back-prop	$0.00$	$81.40$	failed ( rep2 )
Reward-LoRA (surgical zero, § O.4 )	this work, training-free	$0.00$	$\mathbf{7.40}$	not tested

Appendix

Table 28: Comparison with the production DPO LoRA. DPO+L2+SAM (this work) is trained on explicit (chosen, rejected) preference pairs that are assembled automatically from the outputs of reward-back-prop samplers, without human labels. Production DPO (human labels) is the

3

-month production DPO LoRA, trained on human-labelled preference pairs and validated on the real vehicle in

2026

04

Model	cutin (42)	cutout (8)	decel (4)
Base (no LoRA)	$\mathbf{17.0}$	$\mathbf{0.2}$	$\mathbf{48.0}$
Reward-back-prop (reward-LoRA)	$39.8$	$4.5$	$67.0$
Reward-LoRA (surgical zero) (§ O.4 )	$27.4$	$0.7$	$59.1$
DPO+L2+SAM (ours)	$18.5$	$1.0$	$53.5$

Appendix

Table 29: Collision rates in the AWSIM-Script adversarial scenarios, aggregated over the full

54

-script library, with

n{=}200

ODD-Kashiwa scenes per scenario. Cut-in aggregates

42

scripts spanning

V_{e}\in[20,50]\text{km/h}

V_{o}\in[10,40]\text{km/h}

V_{y}\in[0.6,1.6]\text{m/s}

and

dx_{0}\in[5,17]\text{m}

; cut-out aggregates

8

scripts; deceleration aggregates

4

, in which the NPC brakes at

1

G from

V_{o}\in\{20,30,40,50\}\text{km/h}

. Entries are the mean collision % across the scripts of each family. Table 30 gives the results for the five canonical scripts.

Model	ci30-10-6	ci40-20-3	ci20-10-1	co50-1	decel20
Base (no LoRA)	$\mathbf{35.0}$	$\mathbf{17.0}$	$\mathbf{41.0}$	$\mathbf{0.0}$	$\mathbf{73.5}$
Reward-back-prop (reward-LoRA)	$63.0$	$39.0$	$65.5$	$0.0$	$81.5$
Reward-LoRA (surgical zero) (§ O.4 )	$50.5$	$30.0$	$54.0$	$0.0$	$78.5$
DPO+L2+SAM (ours)	$40.0$	$17.5$	$42.5$	$0.0$	$82.0$

Appendix

Table 30: Per-script results on the five canonical scripts from the original AW-Runtime-Verification publication, with

n{=}200

ODD-Kashiwa scenes per script, for comparison with the earlier pilot with

n{=}50

. The models are those of Table 29 .

Figure 10: Mean collision % over the full AWSIM-Script library of

54

scenarios (

n{=}200

ODD-Kashiwa scenes per scenario,

43{,}200

inferences), aggregated by family (cut-in:

42

variants; cut-out:

8

; deceleration:

4

Figure 11: Collision % for each scenario of the AWSIM-Script library ( $54$ scripts, $n{=}200$ scenes per scenario). Rows are models; columns are the $54$ scripts, grouped by family and ego speed (number of scripts in parentheses). Darker cells have higher collision rates.

Figure 12: Heatmap of $TTC_{p25}$ in the cut-in scenarios on a $7$ ( $dx_{0}$ , m) $\times$ $6$ ( $V_{o}$ , km/h) grid, with $V_{y}{=}1.6$ m/s, $V_{e}{=}1.5\,V_{o}$ and $n{=}15$ ODD-Kashiwa scenes per cell. Cell labels report TTC p25 in seconds (5+ means at least $5$ s); darker cells are more dangerous.

Family ( $\#$ scripts)	DPO+L2+SAM	$+$ Adv ( $162$ pairs)	$+$ Adv ( $500$ pairs)	$\Delta$ ( $500$ vs. base)
cutin ( $42$ )	$18.51\%$	$19.57\%$	$\mathbf{17.07\%}$	$-1.44$ pp
cutout ( $\phantom{0}8$ )	$1.00\%$	$0.06\%$	$\mathbf{0.00\%}$	$-1.00$ pp
decel ( $\phantom{0}4$ )	$53.50\%$	$54.75\%$	$\mathbf{51.12\%}$	$-2.38$ pp
peak decel p95 (m/s 2 )	$1.20$	$2.20$	$\mathbf{4.04}$	$+2.84$
# scripts improved vs. base	—	$13/54$	$\mathbf{31/54}$	—
natural-data comfort (n=500)	$0.00\%$	$0.00\%$	$0.00\%$	$\pm 0.00$

Appendix

Table 31: Training with adversarial pairs from the AWSIM-Script library, for two sizes of the adversarial pool. Evaluation uses

n{=}200

validation scenes per scenario that are disjoint from training (

10{,}800

inferences per model). DPO+L2+SAM+Adv starts from DPO+L2+SAM and adds

162

adversarial pairs to the

1500

natural pairs (

\sim\!10\%

adversarial). DPO+L2+SAM+Adv (scaled) uses

500

adversarial pairs (

\sim\!25\%

adversarial). In the last column and in the row of improved scripts, base denotes this starting model, not the base planner.

Figure 13: Effect of training with adversarial pairs (

n{=}200

disjoint validation scenes per scenario,

10{,}800

inferences per model). Left: collision % by family for DPO+L2+SAM, DPO+L2+SAM+Adv (

162

pairs) and DPO+L2+SAM+Adv (scaled,

500

pairs). Right: per-scenario difference between DPO+L2+SAM+Adv (scaled) and DPO+L2+SAM for all

54

scripts, sorted by family.

configuration	lateral offset (m)	jerk-p95	lat-acc-p95	exit-%	progress (m)
shared module only (no expert)	$24.89$	$1323$	$44.31$	$\phantom{0}95.8$	$164.3$
static default (ODD-Nagoya)	$16.04$	$\phantom{0}970$	$54.40$	$100.0$	$163.7$
joint-replay (inherit-shared)	$\phantom{0}6.95$	$\mathbf{\phantom{0}719}$	$52.25$	$100.0$	$\mathbf{186.9}$
joint-replay (from-scratch r=4)	$\mathbf{\phantom{0}4.35}$	$\phantom{0}848$	$\mathbf{23.47}$	$\mathbf{\phantom{0}50.0}$	$178.1$

Appendix

Table 32: Trajectory diagnostics on the

24

-scene held-out target-region pool. The quantities are computed in open loop from a single deterministic DPM-Solver

++

rollout per scene; they are proxies for comfort and corridor compliance, not closed-loop safety measurements. Jerk and lateral acceleration are unsmoothed finite differences of the raw

10

Hz plan, so only comparisons between models are meaningful; exit-% is the share of rollouts that leave a straight

\pm 3

m band along the start lanelet. Of the

10

Ishiodai scenes,

7

are in the training set of both joint-replay checkpoints (§ 4 ).

Figure 14: Real-world topologies of the three held-out target-region maps. Every training ODD has paired opposing lanes. This structure is preserved on Knowledge Hub (research campus) and Ishiodai (suburban district) but absent on Morikoro (open park), which is the geometric source of the

31.9

m lateral offset of the static default analysed in § 4 .

Region	$n$	Hongo	Kashiwa	Shalun	Nagoya	Shared only	Nearest	Best
		Fixed expert (ODD-)
Suburb near ODD-Kashiwa	$30$	$19.70$	$12.70$	$15.90$	$\mathbf{11.33}$	$15.59$	Kashiwa	Nagoya
Urban area nearest ODD-Hongo †	$10$	$38.62$	$\mathbf{8.61}$	$13.97$	$8.65$	$14.60$	Hongo	Kashiwa

Appendix

Table 33: Mean maximum lateral offset (m) of each fixed expert in two regions where the static default does not select ODD-Nagoya. Bold: best fixed expert. The static default selects the nearest expert. † Data from this area were used to train the shared module.

Autonomous Driving Planning

Autonomous driving planning selects safe, feasible vehicle actions and trajectories amid traffic, uncertainty, road rules, and changing goals.

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Oct 26, 2026

Adapt for Planning, Not just Prediction: Optimistic Test-Time World Model Adaptation

Latent world models are typically pre-trained offline and kept frozen at test time, so planning with them can degrade under distribution shift. Test-time adaptation (TTA) can mitigate this degradation by updating the model during deployment. Unlike pre-training on fixed data, TTA for planning is closed-loop: the planner uses model rollouts to select actions, and the resulting transitions drive the next update. This raises the question: which objective should guide TTA for planning? Under a prediction-only objective, the model is fit only to the outcomes of its own actions, so it can remain wrong about the actions that would reach the goal, and low prediction error need not translate into better planning. Inspired by reward-biased maximum likelihood from adaptive control, we introduce Optimistic Test-Time Adaptation (OpTTA). Its objective has two terms, the prediction loss on observed transitions and the planner's goal-reaching cost on its candidate rollouts, both minimized over the model parameters. The planning term biases adaptation toward models that are optimistic about reaching the goal, without any additional environment interaction. Across visual and environment shifts on manipulation, reaching and navigation tasks, OpTTA raises final planning success over the frozen model by 13.5 percentage points on average, compared with 6.9 for the prediction-only objective (AdaJEPA), when only the predictor is adapted. When the encoder is adapted as well, the gains are 13.5 and 7.5 points. These experiments span three JEPA world models with different encoders and training objectives and, for temporal straightening, both CEM and gradient-based planners. Our results suggest that test-time adaptation of world models for planning benefits from an optimistic, task-aware term in addition to the prediction loss.

Akshay Mete, Dileep Kalathil, P. R. Kumar

ECE Department, Texas A&M University, College Station, Texas, USA.

Test-Time Adaptation World Model-Based Planning Latent-Space Planning

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Oct 27, 2026

ExecDiffuser: Closing the Sample-to-Execution Gap in Diffusion Planning

Generative planners are often evaluated by the trajectories they can generate, although closed-loop driving ultimately depends on the single candidate committed to control. We identify this mismatch as the sample-to-execution gap and show that improving proposal quality alone can worsen the executed decision. Here, we introduce ExecDiffuser, a recurrent proposal-to-execution framework that couples candidate generation, trajectory selection, and subsequent replanning through shared execution semantics. Intent-Guided Diffusion Proposal (IGD) assigns hypothesis responsibility and shapes trajectories with execution-conditioned supervision. Execution-Grounded Selection (EGS) learns a candidate-conditioned publication utility, commits one trajectory to control, and returns it as context for the next planning cycle. Across nuPlan, InterPlan, and NAVSIM, ExecDiffuser achieves leading closed-loop performance against strong state-of-the-art baselines. Under a unified five-seed protocol, it obtains an average score of 85.62, improving over Diffusion Planner and FlowDrive by 4.02 and 1.31 points, respectively. On NAVSIM, it achieves 92.6 PDMS under the official evaluation pipeline. Matched counterfactual analysis further shows that ExecDiffuser more reliably converts strong candidates into committed decisions, while prefix interventions confirm that this advantage persists after physical execution and subsequent replanning.

Shuo Pei, Bosun Liang, Saihui Zha +3

Shuo Pei, Saihui Zha, Huachun Tan are with the Beijing Institute of Technology, Guangdong, China. · Shuo Pei, Bosun Liang, Chen Sun, and Yong Wang (Corresponding author) are with the Department of Data and Systems Engineering, The University of Hong Kong, Hong Kong, China.

Autonomous Driving Planning Diffusion-Based Planning Trajectory Generation Dynamic Replanning Diffusion Guidance

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May 11, 2026

Muninn: Your Trajectory Diffusion Model But Faster

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.

Gokul Puthumanaillam, Hao Jiang, Ruben Hernandez +4

University of Illinois Urbana-Champaign. · Florida International University. · Providence College.

Trajectory Generation Diffusion-Based Planning Diffusion Model Caching Robot Motion Planning Diffusion Model Inference Acceleration

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Abstract

Autonomous Driving Planning

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