How Much Can Best-of-N Help a World Action Model? Measuring Selectable Headroom and Realizing It in Closed Loop

Haojia Gao; Yue Cao; Yumin Liu; Haohua Que; Mingkai Liu; Guanqiu Guo; Zhuo Zou; Bokui Chen

cs.ROOct 27, 2026

How Much Can Best-of-N Help a World Action Model? Measuring Selectable Headroom and Realizing It in Closed Loop

Authors: Haojia Gao, Yue Cao, Yumin Liu, Haohua Que, Mingkai Liu, Guanqiu Guo, Zhuo Zou, Bokui Chen,

Organizations: Tsinghua University · Everwise-Tech Co., Ltd. · Fudan University · Research Institute of Tsinghua University in Shenzhen ·

Abstract

World action models (WAMs) predict the visual consequences of the actions they generate, which makes test-time selection a natural way to improve a fixed policy: imagine the futures of candidate actions and execute the best one. The benefit of selection is bounded by the selectable headroom, how much better the best candidate truly is, but the standard estimate, which executes each candidate once and keeps the best outcome, conflates candidate quality with the randomness of everything that follows. We introduce a denoised counterfactual protocol, based on bitwise-reproducible branching, repeated continuations, held-out oracles, and common random numbers, that measures the headroom a selector can realize, and use its measurements to build a fail-gated selector. Across four WAMs, two benchmarks, over 100,000 branched rollouts, and pre-registered tests, we find that (i) the standard estimate overstates the selectable headroom of native samples: bounds from 17 continuations per candidate place its selectable share between 24% and 66% for three WAMs; (ii) structured action perturbations create up to 16 points of selectable headroom; and (iii) in both WAMs with action-conditioned imagination, imagined futures carry candidate-outcome information with no detectable loss relative to real futures, information that the value head of Cosmos Policy leaves unused. Deviating from the policy chunk only when a readout of the WAM predicts failure, the selector raises closed-loop task success from 76.9% to 81.6% on held-out episodes of training tasks, with the largest gain where the policy fails most often, and from 62.6% to 69.8% on unseen tasks.

Figures & tables

Figure 1: How much of the measured headroom is selectable? Orange: the single-continuation oracle (best realized outcome). Blue: the held-out oracle, which selects on three continuations and is scored on a fresh one. Percentages: the held-out share

\bar{O}^{L}/\bar{O}^{1}

, a lower bound on the selectable share. For native samples (a), this share is at most 22% on both benchmarks and for all four models; for structured action perturbations (b), it is 67–95%. Error bars: 95% CIs from a bootstrap clustered by state.

Figure 2: Overview. (a) From a bitwise-reproducible snapshot at $s_{t_{b}}$ , each of $K$ candidate chunks is executed and continued $J$ times by the policy. $O^{1}$ (orange) takes the best realized outcome in each column; $O^{L}$ (blue) selects on the other columns and scores on the held-out one. Here every column contains a success, yet only one candidate succeeds in every continuation. (b) At steps 0, 32, and 64, a failure gate reads the representation of the imagined policy chunk $a$ ; only when its score $q$ exceeds $\theta$ are twelve axis offsets of $a$ imagined with the same noise and ranked. Both readouts are trained on branch outcomes (dashed) rather than taken from the value head; the frames in (b) come from the episode of Fig. 5 .

Figure 3: Headroom versus the number of candidates under the protocol of Yuan et al. [53] (three RoboCasa tasks, 16 native candidates, continuation seeds shared across candidates). The single-continuation oracle keeps rising with

K

, whereas the held-out oracle stays near zero. Shading: 95% CIs.

Figure 4: Candidate-outcome information in imagined and real futures. Each row is a task and a proposal. Blue and orange: linear probes of the frozen representation of Cosmos Policy (last row: Streaming-WAM on 192 new states) for the imagined and the real future (RoboCasa:

s_{t_{b}+32}

; LIBERO-Plus: the state after the executed chunk), with the global direction removed. Green: the value head without additional training.

\star

: pre-registered test.

Single decision points (E9)			Gain
Gate $+$ random offset			$-1.9\,[-3.5,-0.3]$
Gate $+$ best fixed direction †			$+0.1\,[-1.0,1.3]$
Gate $+$ learned ranker †			$+2.0\,[0.7,3.4]$
Closed loop (E8, E10)	Policy	$+$ Selector	Difference
Training tasks, all episodes †	76.9	81.6	$+4.7\,[1.9,7.6]$
Training tasks, robot initial states	65.1	75.8	$+10.7\,[5.4,16.3]$

Table 1: Fail-gated selector versus the policy (Cosmos Policy on LIBERO-Plus; differences in points with 95% CIs). Top: gain per decision point on 400 new states (the gate fires at 45% of them). Bottom: closed-loop task success (three replicates per episode, common random numbers) on reserved episodes of the training tasks and of tasks absent from the training of the selector (the WAM checkpoint is the same). † Pre-registered test.

Figure 5: Closed-loop example on an unseen task (both runs share all seeds). (a) At $t=0$ , the gate fires on the policy chunk $a$ , and the ranker selects $c^{*}$ , the upward offset with $\kappa=0.5$ ; imagined frames next to the real frames 16 steps later. (b) The policy does not lift the bowl from the drawer and times out; the selector succeeds without deviating again. The episode is the first, in hash order, of the 62 in which the policy fails and the selector succeeds in all three replicates; the first of the 26 reverse cases is in Fig. 12 (the appendix).

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Test	Hypothesis and criterion	Outcome
Imagined-future probe, TurnOnStove (E2)	The imagined-future probe ranks perturbed candidates on TurnOnStove at $\kappa=0.25$ and $0.5$ ; criterion: permutation $p<0.025$ and CI lower bound $>0$	Supported: $\rho=+0.31$ ( $p=0.001$ ) and $+0.37$ ( $p=0.0005$ )
Held-out share, replication (E3)	Ratio $R^{L}$ of the held-out to the single-continuation oracle; premise: at least 15 weighted decision points and a CI lower bound of $\bar{O}^{1}$ above 0; criterion: upper CI bound $<0.5$	Supported: $R^{L}=0.086\,[-0.009,0.270]$ ; secondary test $\bar{O}^{L}>0$ : $p=0.12$
Onset of readability (E4)	The perturbation scale at which outcomes become readable on TurnOnStove (readable at $\kappa=0.5$ with $p<0.0125$ , not at $\kappa=0.1$ ) transfers to TurnOnMicrowave and PnPCounterToSink	Not supported, because readability can appear earlier: TurnOnMicrowave is readable already at $\kappa=0.1$ ( $\rho=+0.31$ , $p=0.028$ ) and at $\kappa=0.5$ ( $+0.54$ , $p=0.0005$ ); PnPCounterToSink at $\kappa=0.5$ : $\rho=+0.17$ , $p=0.032$ . The onset of readability depends on the task ( Appendix F )
Value head on real states (E4)	A value head that scores real post-action states selects better candidates than one that scores imagined futures	Not supported, consistent with Sec. 5.3 : value heads rank candidates poorly whatever their input (gain $+0.014$ , $p=0.20$ ; paired difference $+0.001\,[-0.044,0.049]$ )
Held-out share, three WAMs (E5)	$R^{L}$ pooled over the WAMs that meet the premise of the replication test; criterion: upper CI bound $<0.5$	Supported: all three models meet the premise; pooled $R^{L}=0.134\,[0.024,0.260]$ ; per model 0.145, 0.177, and 0.092, each with an upper bound $<0.5$
Structured headroom (E6)	Held-out oracle among seven candidates minus the policy chunk at $\kappa=0.5$ , per model; criterion: CI lower bound $>0$	Supported for both models: Cosmos Policy $+0.112\,[0.046,0.196]$ ; Flex- $\pi$ $+0.045\,[0.006,0.096]$

Appendix

Table 2: All pre-registered tests and their outcomes, in the order of registration.

Test	Hypothesis and criterion	Outcome
Structured headroom, Streaming-WAM (E6)	As the structured-headroom test, for Streaming-WAM; criterion: CI lower bound $>0$	Not supported: $+0.045\,[-0.010,0.116]$ ; its policy chunk succeeds at 85% of these decision points (66–75% for the other models), and 78% of the single-continuation gain survives held-out evaluation ( Appendix E )
Imagined-future probe, Streaming-WAM (E6)	Imagined-future probe (specification of the LIBERO-Plus probe; imagination conditioned on the first 8 executed steps); criterion: on some arm, permutation $p<0.025$ and CI lower bound $>0$	Not supported: both arms meet the premise; $\rho=0.079$ ( $p=0.32$ ) at $\kappa=0.1$ and $0.110\,[-0.014,0.243]$ ( $p=0.10$ ) at $\kappa=0.5$ ; the probe of the real future reaches $0.162$ ( $p=0.037$ ) at $\kappa=0.5$ ( Appendix F )
Imagined versus real probe, Streaming-WAM (E6)	As the imagined-versus-real test, for Streaming-WAM; criterion: CI within $[-0.15,0.15]$	Supported: $-0.005\,[-0.146,0.129]$
Held-out share, Streaming-WAM (E5)	$R^{L}$ for Streaming-WAM, with the premise of the replication test; criterion: upper CI bound $<0.5$	Supported: $R^{L}=-0.087\,[-0.227,0.052]$ (53 decision points); pooled with the other three models, $0.095\,[-0.008,0.213]$ (descriptive)
In-sample share, Flex- $\pi$ (E5 + )	In-sample oracle over 17 continuation schedules as a share of $\bar{O}^{1}$ (Flex- $\pi$ , 16 native candidates); criterion: upper CI bound $<2/3$ , that is, an overstatement of at least 1.5-fold	Not supported: $0.658\,[0.546,0.787]$ , so the overstatement is at least 1.27-fold at 95% confidence; the held-out share with 16 selection schedules is $0.334\,[0.146,0.504]$ ( Fig. 6 )
In-sample share, Fast-WAM (E5 + )	As the previous test, for Fast-WAM	Not supported: $0.626\,[0.499,0.786]$ , so the overstatement is at least 1.27-fold at 95% confidence; the held-out share with 16 selection schedules is $0.331\,[0.148,0.506]$

Appendix

Table 3: Pre-registered tests that extend the measurements to Streaming-WAM and to 17 continuations for Flex-

\pi

and Fast-WAM (continued from Tab. 2 ).

Set	Tasks (states)	$t_{b}$	Candidates	Continuations	Rollouts
E1	TurnOnStove, PnPCounterToCab (17)	0/48/96/144	6 native; random offsets	independent, $J{=}4$	2.4k
E2	TurnOnStove (40), PnPCounterToCab (20)	0/96	chunk $+$ 6 axis offsets, $\kappa\in\{0.1,0.25,0.5\}$ ; native	independent, $J{=}4$	9.3k
E3	TurnOffStove, PnPCounterToSink, TurnOnStove (7 each)	0/16/32/48	16 native	shared schedule, $J{=}1{+}4$	3.9k
E4	TurnOnMicrowave, PnPCounterToSink (25 each)	0/96	chunk $+$ 6 axis offsets, $\kappa\in\{0.1,0.5\}$	independent, $J{=}4$	5.6k
E5	LIBERO-Plus, 4 WAMs (80 shared)	first query, step $\geq$ 80	16 native	shared schedule, $J{=}1{+}4$	21.5k
E5 +	LIBERO-Plus, Cosmos Policy, Flex- $\pi$ , and Fast-WAM, all second-stage points of E5 (37, 40, 35)	as E5	16 native	shared schedule, $J{=}17$	26.1k

Appendix

Table 4: Branching datasets. “States” counts trunks; each trunk contributes decision points at the listed

t_{b}

Ratio	DPs	States	$O^{1}>0$	Top-5	Est.	LOSO range
E3 $R^{L}$	36	18	19	0.43	0.086	$[0.030,0.130]$
E5 $R^{L}$ , Cosmos	46	37	21	0.49	0.145	$[0.112,0.194]$
E5 $R^{L}$ , Flex- $\pi$	46	40	18	0.61	0.177	$[0.062,0.246]$
E5 $R^{L}$ , Fast-WAM	44	35	20	0.59	0.092	$[0.033,0.173]$
E5 $R^{L}$ , Streaming-WAM	53	41	16	0.66	$-0.087$	$[-0.119,-0.036]$
E5 $R^{L}$ , pooled (first three)	136	112	59	0.27	0.134	$[0.107,0.162]$

Appendix

Table 5: Effective sample size and leave-one-state-out (LOSO) stability of the headline ratios. Top-5: share of the weighted

\bar{O}^{1}

carried by the five largest decision points. For the pooled row, States counts model–state pairs, and LOSO leaves out one such pair; the CIs of pooled estimates in the main text instead resample shared states.

Figure 6: Bracketing the selectable share (E5 + : Cosmos Policy (a), Flex-

\pi

(b), and Fast-WAM (c) on LIBERO-Plus, 16 native candidates, 17 shared continuation schedules). Blue: held-out oracle that selects on

m

schedules and is scored on another, as a share of the single-continuation oracle; its expectation is a lower bound. Orange: in-sample oracle over all 17 schedules; its expectation is an upper bound. Green: model-based extrapolation to

m\to\infty

(exploratory). Bands and bars: 95% CIs.

Figure 7: Variance decomposition of outcomes on E3 , the protocol of Yuan et al. [53] (16 native candidates, continuation seeds shared across candidates): the candidate effect is negligible next to the candidate

\times

continuation interaction. The headroom versus the number of candidates on the same data is shown in Fig. 3 .

	Native		Structured, $\kappa=0.5$
Model	$\bar{O}^{1}$	Held-out share	Oracle $-$ chunk	Share
Cosmos Policy	0.073	0.15 $[0.02,0.30]$	$+0.112\,[0.046,0.196]$	0.95
Flex- $\pi$	0.047	0.18 $[-0.14,0.48]$	$+0.045\,[0.006,0.096]$	0.79
Fast-WAM	0.073	0.09 $[-0.05,0.33]$	$+0.088\,[0.034,0.157]$	0.86
Streaming-WAM	0.031	$-0.09$ $[-0.23,0.05]$	$+0.045\,[-0.010,0.116]$	0.78
Streaming-WAM, E11			$+0.052\,[0.026,0.083]$	0.80

Appendix

Table 6: LIBERO-Plus summary. Native: 16 native candidates with shared continuation schedules (E5). Structured: policy chunk

+

6 axis offsets at

\kappa=0.5

(E6; E11 for 192 new states). Held-out share:

\bar{O}^{L}/\bar{O}^{1}

with three outcomes per candidate, whose expectation is a lower bound on the selectable share. All test quantities except the four-model pool were pre-registered; 95% CIs from a bootstrap clustered by state.

Set	DPs	Model chunk	Executed actions	Global medoid	Held-out oracle
		KeyStone
E3 (RoboCasa, Cosmos Policy)	36	$+0.006\,[-0.002,0.015]$	$+0.010\,[-0.005,0.029]$	$+0.024\,[0.002,0.050]$	$+0.009\,[-0.003,0.026]$
E5, Cosmos Policy	46	$-0.007\,[-0.021,0.005]$	$-0.006\,[-0.018,0.005]$	$-0.010\,[-0.025,0.003]$	$+0.011\,[0.002,0.024]$
E5, Flex- $\pi$	46	$-0.002\,[-0.011,0.006]$	$+0.007\,[0.002,0.013]$	$+0.010\,[-0.002,0.025]$	$+0.008\,[-0.006,0.027]$
E5, Fast-WAM	44	$-0.003\,[-0.021,0.013]$	$+0.014\,[-0.000,0.029]$	$-0.007\,[-0.031,0.014]$	$+0.007\,[-0.004,0.020]$
E5, pooled	136	$-0.004\,[-0.012,0.004]$	$+0.005\,[-0.002,0.011]$	$-0.002\,[-0.013,0.008]$	$+0.009\,[0.002,0.017]$

Appendix

Table 7: Judge-free selection on native candidates. KeyStone [ 10 ] with its default settings (L2 distance, unimodality threshold 0.3, two clusters, and the medoid of the larger cluster; mean over 20 seeded k-means initializations), applied offline to the 16 native candidates of each second-stage decision point. Gain: success rate of the chosen candidate minus the candidate mean, with two-stage weights; 95% CIs from a bootstrap clustered by state. The main analysis uses the action chunk of the model (for Flex-

\pi

, the seven dimensions that reach the environment); the executed actions serve as a sensitivity analysis.

Figure 8: Headroom over the policy chunk on RoboCasa. Blue: held-out oracle minus the policy chunk. Orange: the average perturbed candidate minus the policy chunk. Structured perturbations create selectable headroom on TurnOnStove, TurnOnMicrowave, and PnPCounterToSink; because the average perturbed candidate is worse than the policy chunk, the gain is available only to a selector. Hollow markers: 5 states, without error bars.

Model	Policy	Fails	Gain where it fails	Elsewhere
Cosmos Policy	0.75	26%	$+0.44\,[0.20,0.88]$	$-0.004$
Flex- $\pi$	0.75	25%	$+0.21\,[0.07,0.48]$	$-0.010$
Fast-WAM	0.66	41%	$+0.21\,[0.08,0.39]$	$+0.006$
Streaming-WAM	0.85	17%	$+0.38\,[0.13,0.83]$	$-0.022$
Streaming-WAM, E11	0.85	19%	$+0.27\,[0.14,0.43]$	$+0.003$

Appendix

Table 8: Where the structured headroom lies (E6 and E11,

\kappa=0.5

; exploratory). Policy: success of the policy chunk. Fails: share of pairs of a decision point and a scoring continuation in which the policy chunk fails in at least one of the other three continuations. Gain: held-out oracle minus the policy chunk on the scoring continuation, split by this condition; 95% CIs from a bootstrap clustered by state.

Value head	AUROC	$\rho$	Gain	Cons.	$\rho$	Gain	Cons.
		Native			Perturbed ( $\kappa{=}0.1$ )
Public	0.53	$+0.05$	$-0.001$	0.72	$+0.02$	$-0.067$	0.94
Tuned 5K	0.87	$+0.03$	$-0.001$	0.74	$+0.02$	$-0.006$	0.78
Tuned 10K	0.90	$+0.03$	$+0.008$	0.84	$+0.18$	$+0.001$	0.86
Tuned 15K	0.90	$+0.02$	$+0.003$	0.72	$+0.11$	$+0.001$	0.84

Appendix

Table 9: Value heads value states, not candidates (E1, common random numbers,

s^{\prime}=s_{t_{b}+16}

). AUROC: state value versus final success.

\rho

: within-decision Spearman correlation between

\bar{V}

and

\hat{p}

. Gain: success gain of selecting by

\bar{V}

over the candidate mean. Cons.: within-decision rank agreement across three value seeds.

Figure 9: Imagined versus real futures of seven sibling candidates (Cosmos Policy, $\kappa=0.5$ ; for each benchmark, the first decision point by index among those with the largest outcome range). Columns: the policy chunk and its six axis offsets; $\hat{p}$ : success rate over four continuations (orange: $\hat{p}<0.5$ ); $V$ : value head on the imagined future. On RoboCasa, the imagined frames reproduce the direction-specific consequences, such as the kettle entering the view under $-y$ and the higher viewpoint under $+z$ , at lower sharpness and with smaller displacements than the real ones. On LIBERO-Plus, the imagined views closely match the real ones, including the basket edge that appears only under the failing $+y$ offset.

Condition	DPs	Future	Action	Fut $\|$ act	Act $\|$ fut	Fut $\|$ state $\times$ dir	Value frame
TurnOnStove $\kappa{=}0.1$	40	$-$ 0.19	$-$ 0.09	$-$ 0.15	+0.17	$-$ 0.25	$-$ 0.01
TurnOnStove $\kappa{=}0.25$	53	+0.31	+0.17	+0.08	+0.05	+0.14	+0.22
TurnOnStove $\kappa{=}0.5$	59	+0.37	+0.19	+0.16	$-$ 0.05	+0.29	+0.19
PnPCounterToCab $\kappa{=}0.1$	19	+0.20	+0.07	+0.14	$-$ 0.06	+0.06	+0.30
PnPCounterToCab $\kappa{=}0.25$	20	+0.23	+0.03	+0.25	$-$ 0.15	+0.16	+0.04
PnPCounterToCab $\kappa{=}0.5$	23	+0.06	+0.11	$-$ 0.14	+0.18	+0.03	$-$ 0.07

Appendix

Table 10: Readout by latent frame of the imagination pass (within-decision Spearman correlation with the outcome).

$a$	$\tau=0$	$0.02$	$0.05$	$0.1$	$0.15$	$0.2$
0.1	$-0.055$	$-0.055$	$-0.055$	$-0.054$	$-0.051$	$-0.047$
1	$-0.053$	$-0.052$	$-0.054$	$-0.053$	$-0.050$	$-0.047$
10	$-0.043$	$-0.043$	$-0.042$	$-0.042$	$-0.037$	$-0.035$
100	$-0.030$	$-0.030$	$-0.028$	$-0.024$	$-0.021$	$-0.019$

Appendix

Table 11: Ranking with abstention: cross-validated gain over the policy chunk on E7 (696 decision points, 13 candidates) over the pre-registered grid of

a

and

\tau

Variant	Gain	Diff.
Full model (recipe of the frozen selector)	$+0.025\,[0.009,0.041]$	—
Gate: current-observation frames only	$+0.025\,[0.009,0.041]$	$+0.000\,[-0.002,0.002]$
Gate: imagined future frames only	$+0.025\,[0.009,0.042]$	$+0.000\,[-0.008,0.007]$
Gate: value-head scalar only	$+0.007\,[-0.004,0.019]$	$+0.018\,[0.004,0.031]$
Ranker: imagined future frames only	$+0.020\,[0.005,0.035]$	$+0.005\,[-0.004,0.014]$
Ranker: action frame only	$+0.018\,[0.004,0.033]$	$+0.007\,[-0.006,0.019]$

Appendix

Table 12: What the fail-gated selector relies on. Nested cross-validation on E7 (696 decision points; the same outer folds as for the frozen selector), changing one ingredient at a time; gain over the policy chunk with two-stage weights; 95% CIs from a bootstrap clustered by state (by base task for task folds). Diff.: full model minus the variant, paired over decision points.

Figure 10: Gain versus imagination cost (E7, nested cross-validation; exploratory). The gate and the ranker of each outer fold are those selected by the inner cross-validation, and only the gate threshold is swept. Cost: imagination passes per decision point, that is, twelve times the share of decision points at which the gate fires. Star: the thresholds selected by cross-validation; square: the gate always fires. Band and bar: 95% CIs from a bootstrap clustered by state.

Figure 11: Closed-loop gain on each unseen task (E10: Cosmos Policy on LIBERO-Plus, robot initial states; 10–33 episodes per task, three replicates per episode with common random numbers). (a) Success rate of the selector that never saw the task minus that of the policy (bars; 95% CIs from a bootstrap over the episodes of the task), and the same difference for the selector trained on all tasks (diamonds); tasks are sorted by the first difference. (b) The first difference against the success rate of the policy on the same task.

Figure 12: Closed-loop counterexample on an unseen task (E10: “put the cream cheese in the bowl”; the first, in hash order, of the 26 episodes in which the policy succeeds and the selector fails in all three replicates; both runs share all seeds). Top: the policy succeeds; the selector deviates at $t=0$ , 32, and 64 and times out. Bottom: at each deviation, imagined frames and the real frames 16 steps after executing the policy chunk $a$ or the selected offset $c^{*}$ from the state of the selector run. Because the two runs separate at $t=0$ , the real frames for $a$ at $t=32$ and 64 come from a 16-step branch from that state, not from the policy run.

Task	$\kappa$	States	Held-out oracle	Fixed direction	Imagined probe	Real $s_{t_{b}+32}$ probe	Value head
TurnOnStove	0.25	35	$+0.158$	$-0.006$	$+0.008$	$-0.006$	$+0.014$
TurnOnStove	0.5	36	$+0.112$	$\phantom{+}0.000$	$-0.017$	$-0.070$	$-0.090$
PnPCounterToCab	0.5	15	$+0.027$	$\phantom{+}0.000$	$-0.055$	$-0.098$	$-0.226$
PnPCounterToSink	0.5	24	$+0.131$	$-0.052$	$-0.020$	$+0.008$	$-0.020$
TurnOnMicrowave	0.1	18	$+0.070$	$+0.069$	$+0.069$	$+0.036$	$+0.008$
TurnOnMicrowave	0.5	23	$+0.123$	$+0.032$	$+0.097$	$+0.093$	$-0.144$

Appendix

Table 13: Offline selection on RoboCasa in the seven-candidate pool (policy chunk

+

6 offsets); gain over executing the policy chunk. Learned selectors are evaluated leave-one-state-out. Probe: global direction

+

linear residual on the representation.

Selector	Gain	Dev.
Policy chunk	0	0%
Random candidate	$-0.081\,[-0.136,-0.033]$	86%
Value head on the imagined future	$-0.096\,[-0.175,-0.022]$	–
Ranking with abstention	$0\,[0,0]$	0%
Failure gate $+$ random offset †	$-0.040\,[-0.083,-0.004]$	42%
Failure gate $+$ learned ranker †	$+0.020\,[-0.028,0.076]$	42%

Appendix

Table 14: Reference results of the selector track (E6 test split, Cosmos Policy; primary pool: policy chunk

+

6 offsets at

\kappa=0.5

, among which every selector chooses; 69 decision points, 48 states). Gain over the policy chunk with 95% CIs from a bootstrap clustered by state. Dev.: share of decision points at which the selector deviates from the policy chunk. † E6 informed the design of this selector; its held-out evaluation is on E9.

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Jul 20, 2026

Test-Time Scaling for World Action Models via Zero-Shot Geometric Evaluation

Test-time scaling improves foundation-model inference by spending additional computation, but robot control requires deciding whether extra compute is useful before executing an action. World Action Models (WAMs) make this decision natural: each rollout exposes both an action chunk and predicted future observations. We propose \methodgated, a training-free selective test-time scaling framework for WAMs. We first instantiate \method, a fixed-budget Best-of-

N

selector that ranks sampled rollouts by cross-view depth reprojection consistency of their predicted futures, computed with a frozen geometry foundation model. \methodgated\ adds a lightweight action--future consistency gate that invokes \method\ only when the initial rollout appears internally inconsistent. Across five benchmark--backbone settings on RoboCasa, LIBERO Long, and RoboTwin~2.0, fixed-budget \method\ improves

N{=}8

task success in every setting, e.g., raising the RoboCasa group average from

66.3\%

68.4\%

with Cosmos Policy and from

80.8\%

82.5\%

with X-WAM. With gating enabled, \methodgated\ recovers on average

74.8\%

of the always-on success gain while triggering additional sampling on only

26.2\%

of decision points. Offline diagnostics show that cross-view reprojection is a strong task-label-free selector, and we identify false low-score selections as a failure mode that helps explain why performance can saturate or degrade as

N

increases.

Zesen Zhao, Minkyoung Cho, Hui shen +4

University of Michigan · 2NVIDIA

World Models for Robotics World Model-Based Planning Action-Conditioned World Models Test-Time Scaling World Action Models

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May 8, 2026

Is the Future Compatible? Diagnosing Dynamic Consistency in World Action Models

World Action Models (WAMs) enable decision-making through imagined rollouts by predicting future observations and actions. However, the reliability of these imagined futures remains under-examined: is a generated future merely visually plausible, or is it dynamically compatible with the action sequence it claims to model? In this work, we identify action-state consistency, the alignment between predicted actions and induced state transitions, as a missing reliability axis for WAMs. Through a systematic study across representative joint-prediction and inverse-dynamics models, we find that action-state consistency systematically separates successful and failed rollouts across many tasks and follows similar success-failure trends as learned value estimates. These results suggest that consistency captures decision-relevant structure beyond visual realism. We further identify background collapse as an important boundary condition, where low-dynamics failed trajectories can become deceptively consistent because static futures are easier to predict. Building on these findings, we introduce a value-free consensus strategy for test-time selection, which ranks candidate rollouts by agreement among predicted futures. This strategy improves success rates on RoboCasa and RoboTwin 2.0 without additional training or reward modeling. Taken together, our findings establish action-state consistency as both a diagnostic tool for evaluating WAM reliability and a practical signal for value-free planning.

Bo-Kai Ruan, Teng-Fang Hsiao, Ling Lo +1

National Yang Ming Chiao Tung University

World Models for Robotics World Model-Based Planning Model-Based Planning World Action Models World Model Evaluation

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Abstract

World Model-Based Planning

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