CaliBench: Are the Stochastic Dynamics of Video World Models Physically Calibrated?

Jonathan Sadeghi; Jenny Seidenschwarz; Jesse Allardice; Sirish Srinivasan; Benjamin Graham; Jeffrey Hawke

cs.LGAug 17, 2026

CaliBench: Are the Stochastic Dynamics of Video World Models Physically Calibrated?

Authors: Jonathan Sadeghi, Jenny Seidenschwarz, Jesse Allardice, Sirish Srinivasan, Benjamin Graham, Jeffrey Hawke

Organizations: Odyssey

Abstract

Video world models approximate the stochastic distribution of physical outcomes through generative sampling, but existing benchmarks score individual generations or compare distributions coarsely over a whole dataset, leaving the fine-grained aleatoric uncertainty of specific phenomena untested. We introduce CaliBench, which scores outcomes in a physically interpretable discrete space - a bin index, a die face, a suit, a colour - rather than a learned feature space such as in FID, so the distance from a known reference distribution is measured directly. We curate outcome spaces whose reference is known in closed form (binomial Galton boards, Bernoulli forks, uniform dice/cards/lottery, a skewed European-roulette colour), enabling an exact calibration test. We decompose performance into two orthogonal axes that a single accuracy metric conflates: scorability, the fraction of generations yielding a scoreable outcome, and calibration, the total variation distance from the reference on that sample. A chi-squared test assesses significance; as calibration is its null hypothesis it can evidence only miscalibration, and at N=32 per cell detects only large deviations. We apply it to nine scenes and six image-to-video models (WAN-2.7, SeeDance-2.0, HappyHorse-1.0, Veo 3.1, Runway Gen-4.5, Cosmos3-Super), 32 generations each. Models consistently concentrate probability mass on a few outcomes rather than reproducing the reference. Most scene-model combinations are significantly miscalibrated, in the extreme collapsing to one outcome, as Veo 3.1 does on dice. On roulette, generations often leave the ball ambiguously placed, giving several models low scorability. Performance varies by scene: no model dominates all nine. We release the protocol and a metric (mean normalised total variation, mnTV) for comparing new models against our results.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of the CaliBench protocol. (1) Each scene pairs a conditioning frame and text prompt with an analytically known reference distribution over a discrete, interpretable outcome space (e.g. Binomial $(10,\nicefrac{{1}}{{2}})$ over Galton-board bins). (2) A video model generates $N{=}32$ videos from identical inputs, varying only the random seed. (3) A vision–language model (Gemini 3.1 Pro, majority vote of three queries) extracts each video’s discrete outcome from its final frame. (4) We compare the empirical outcome distribution to the reference along two orthogonal axes: scorability $\rho$ (fraction of scoreable generations) and calibration (total variation distance $\mathrm{TV}(\hat{p},p_{0})$ from the reference).

Panel of Figure 2 — Figure 2: Conditioning frames for all nine scenes. Top row (left to right): physical board, animated board [Binomial $(10,\nicefrac{{1}}{{2}})$ ]; ball fork, walking, double pendulum [Bernoulli $(\nicefrac{{1}}{{2}})$ ]. Bottom row: dice, cards, lottery [Uniform]; roulette colour [known non-uniform].

Model	ID	Duration	Resolution	Prompt exp.	Neg. prompt	Audio
WAN-2.7	wan-video/wan-2.7-i2v	3 s	720p	yes	""	N/A
SeeDance-2.0	bytedance/seedance-2.0	4 s	480p	N/A	N/A	off
HappyHorse-1.0	alibaba/happyhorse-1.0	3 s	720p	N/A	N/A	N/A
Veo 3.1	google/veo-3.1	4 s	720p	N/A	unset	on
Runway Gen-4.5	runwayml/gen-4.5	5 s	N/A	N/A	N/A	N/A
Cosmos3-Super	nvidia/Cosmos3-Super (local)	5.04 s †	1280 $\times$ 704	N/A	set	N/A

Table 1: Per-model video-generation settings. All models receive the same conditioning frames, text prompts, and 32 fixed seeds; only the settings below differ. Italic marks a value equal to the provider’s API default (whether we set it explicitly or left it unset); N/A means the model’s API does not expose that parameter. Per-model durations are the shortest length each provider offers; WAN-2.7 (3 s) and SeeDance-2.0 (4 s) accept an arbitrary integer duration and were fixed slightly above the API minimum.

Figure 3: Frame strips from two physical Galton-board video generations illustrating the two outcome categories. Top: a scoreable video generation (HappyHorse): a single ball is released, falls through the peg array, and comes to rest in a single bin. Bottom: an invalid video generation (Veo 3.1): the model generates multiple balls during the simulation, leaving the outcome unscoreable. Failures of this type drive the scorability $\rho$ metric below $1$ .

Binomial $(10,\nicefrac{{1}}{{2}})$ — 11 bins
	WAN-2.7		SeeDance-2.0		HappyHorse		Veo 3.1		Runway 4.5		Cosmos3-Super
Scene	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$
Physical board	0.69	0.71	0.59	0.27	0.88	0.58	0.03	0.99 †	0.56	0.37	0.19	0.50
Animated board	0.91	0.75	0.88	0.66	0.91	0.68	0.97	0.49	0.88	0.20	0.03	0.99 †
Bernoulli $(\nicefrac{{1}}{{2}})$ — 2 outcomes
Ball fork	1.00	0.25	1.00	0.19	0.94	0.00	0.97	0.24	0.91	0.12	0.84	0.06

Table 2: Per-scene–model descriptive results across all nine evaluation environments. We evaluate the Total Variation Distance

\mathrm{TV}

from the scene’s reference distribution on the valid sample (lower is better, range

[0,1]

\dagger

: small

n_{\mathrm{valid}}

(

{\leq}3

), so per-scene–model distributional statements are unreliable. —:

0

valid video generations. Bold: lowest

\mathrm{TV}

per scene among non-

\dagger

cells.

\mathrm{mnTV}

footer:

[2.5\%,97.5\%]

bracketed values are the bootstrap interval from

50{,}000

resamples within each scene–model combination (Appendix A ). Mean Normalised Total Variation (mnTV): mean of

s_{\mathrm{sm}}

across all nine scenes, scene–model decomposition in Appendix A . For reference, a perfectly calibrated, fully scoreable model has

\mathrm{mnTV}\approx 0

(central-

95\%

range

\approx[-0.04,\,0.04]

over

50{,}000

synthetic draws); the observed mnTVs in the footer all sit far above this null range. Pendulum is daggered for all six models — none yields more than three valid generations (Cosmos3-Super three, SeeDance-2.0 two, the rest at most one): a universal structural failure.

Binomial $(10,\nicefrac{{1}}{{2}})$
Scene	WAN-2.7	SeeDance	HappyHorse	Veo 3.1	Runway	Cosmos3-Super
Physical board	0.005	0.088	0.004	$\dagger$	0.038 ‡	0.013
Animated board	$<$ 0.001	$<$ 0.001	0.001	0.057	0.002	$\dagger$
Bernoulli $(\nicefrac{{1}}{{2}})$
Ball fork	0.007	0.051	1.000	0.011	0.264	0.699
Walking	0.0297	0.051	0.214	$<$ 0.001	0.859	1.000

Table 3: Monte Carlo

p

-values from the

\chi^{2}

test against the reference distribution (50,000 null hypothesis (

H_{0}

) replicates per scene–model combination, seed

=0

H_{0}

: outputs are i.i.d. from the reference (calibrated). Values shown are raw

p

-values; we control the false discovery rate across the

44

computed tests with the Benjamini–Hochberg procedure at

\alpha=0.05

(BH critical threshold

p\leq 0.0297

; full raw and adjusted values in Appendix D ).

\dagger

{\leq}3

valid video generations; —: 0 valid video generations.

\ddagger

: significant at raw

\alpha=0.05

but not after Benjamini–Hochberg correction (

q>0.05

Figure 4: Empirical bin distributions for each model (blue) vs. ground-truth Binomial

(10,\nicefrac{{1}}{{2}})

(orange). Top: physical board. Bottom: animated board. Most models over-concentrate near the central bin, far exceeding the expected peak probability of 24.6%; on the animated board SeeDance-2.0 instead places excessive probability mass on the left tail (bin 1 and 2).

Figure 5: Scorability vs. total variation distance

\mathrm{TV}

for all nine scenes. The bottom-right corner of each panel (high scorability, low

\mathrm{TV}

) is the calibration target; no evaluated model approaches it consistently across scenes. The shaded band per panel is the central-

95\%

envelope of

\mathrm{TV}

under perfect calibration at

n_{\mathrm{valid}}=N

, shown as a descriptive aid for interpreting the magnitude of

\mathrm{TV}

relative to sampling noise — it is not a rejection region, and a marker’s position relative to the band is not equivalent to the calibration verdict (which comes from the Monte Carlo exact

\chi^{2}

test). The band is drawn at

n_{\mathrm{valid}}=N=32

per panel and does not directly characterise sampling noise for cells with

\rho<1

(those cells have a wider envelope, not shown). Because of the upward bias of the

\mathrm{TV}

estimator, the shaded null band does not necessarily include

\mathrm{TV}=0

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Binomial $(10,\nicefrac{{1}}{{2}})$
Scene	WAN-2.7	SeeDance	HappyHorse	Veo 3.1	Runway	Cosmos3-Super
Physical board	0.75	0.44	0.54	1.00	0.54	0.84
Animated board	0.73	0.63	0.65	0.39	0.13	1.00
Bernoulli $(\nicefrac{{1}}{{2}})$
Ball fork	0.19	0.13	-0.01	0.21	0.14	0.14
Walking	0.17	0.13	0.06	0.46	-0.04	0.10

Appendix

Table 4: Per-scene–model score

s_{\mathrm{sm}}

(Eq. 9 ), with mnTV (mean across nine scenes) in the bottom row. Lower is better; bounded above by

1

, with

0

the calibrated expectation (small negatives occur for cells better-calibrated than the sampling-noise floor). Bold: lowest per scene; mnTV: lowest overall.

Figure 6: Ball fork scene. Ground truth: Bernoulli

(\nicefrac{{1}}{{2}})

(uniform over left/right). Most models are close to calibrated; small

\mathrm{TV}

values visible as mild left/right imbalance.

Figure 7: Walking (T-junction) scene. Ground truth: Bernoulli

(\nicefrac{{1}}{{2}})

. Similar to the ball fork: most models show mild directional imbalance.

Figure 8: Double pendulum scene. Ground truth: Bernoulli

(\nicefrac{{1}}{{2}})

. Only models with at least one valid video generation appear (SeeDance-2.0 with two, Veo 3.1 with one, and Cosmos3-Super with three; WAN, HappyHorse, and Runway produced none), so panels reflect very few samples.

Figure 9: Dice scene. Ground truth: Uniform

\{1,\ldots,6\}

. Mode collapse is severe for several models, with Veo 3.1 always producing the same face.

Figure 10: Cards scene. Ground truth: Uniform over 4 suits. Scorability failures dominate: five of six models have

\rho<0.6

. SeeDance-2.0 retains the highest scorability (

\rho=0.91

) and has the lowest

\mathrm{TV}

among models with

\rho>0.5

(

\mathrm{TV}=0.50

, still significantly miscalibrated).

Figure 11: Lottery scene. Ground truth: Uniform

\{1,\ldots,20\}

. High cardinality exposes severe collapse: probability mass concentrates on a small number of ball numbers across all models.

Figure 12: Roulette scene. Ground truth:

P(\text{red})=P(\text{black})=\nicefrac{{18}}{{37}}

P(\text{green})=\nicefrac{{1}}{{37}}

. Among models with non-trivial scorability, green is over-represented relative to the reference

2.7\%

in five of six (WAN:

14\%

, SeeDance:

15\%

, Veo 3.1:

5\%

, Runway:

14\%

, Cosmos3-Super:

50\%

6/12

valid); HappyHorse is the exception, producing no green outcomes (

0/31

Scene	Min $\mathrm{TV}$ ( $N=32$ )	Min $\mathrm{TV}$ ( $N=16$ )
Ball / Walking / Pendulum	0.24	0.30
Roulette	0.12	0.20
Cards	0.26	0.36
Dice	0.26	0.37
Galton board	0.49	0.59
Lottery	0.22	0.31

Appendix

Table 5: Minimum Total Variation Distance (

\mathrm{TVD}

) required for the Monte Carlo

\chi^{2}

test to reject the null hypothesis of perfect calibration with

\geq 80\%

power under an extreme-mode contamination alternative. Lower thresholds indicate higher test sensitivity within that environment. The

N=16

column models performance degradation in cells exhibiting a low scorability ratio (

\rho\approx 0.5

Figure 13: Statistical power curves of the Monte Carlo

\chi^{2}

test against total variation distance

\mathrm{TV}

for each scene’s reference distribution, at four sample sizes. Curves use the contamination alternative described above; dashedline marks 80% power.

Scene	Model	raw $p$	$q_{\mathrm{BH}}$	$p_{\mathrm{Bonf}}$
Animated board	SeeDance	$<$ 0.001	$<$ 0.001	$<$ 0.001
Walking	Veo 3.1	$<$ 0.001	$<$ 0.001	$<$ 0.001
Dice	WAN-2.7	$<$ 0.001	$<$ 0.001	$<$ 0.001
Dice	SeeDance	$<$ 0.001	$<$ 0.001	$<$ 0.001
Dice	HappyHorse	$<$ 0.001	$<$ 0.001	$<$ 0.001
Dice	Veo 3.1	$<$ 0.001	$<$ 0.001	$<$ 0.001

Appendix

Table 6: Raw Monte Carlo

\chi^{2}

p

-values for all

44

tested scene–model cells (sorted ascending), with Benjamini–Hochberg adjusted

p

-values (

q_{\mathrm{BH}}

, FDR control) and Bonferroni-adjusted

p

-values (

p_{\mathrm{Bonf}}

, FWER control) over the family of

44

tests.

\ddagger

marks the cells significant at raw

\alpha=0.05

but not after BH correction.

Scene	Model	$\rho$	TV best	TV worst	TV rep
Cards	WAN-2.7	0.56	0.219	0.656	0.766
Cards	SeeDance-2.0	0.91	0.406	0.500	0.547
Cards	HappyHorse-1.0	0.38	0.000	0.562	0.812
Cards	Veo 3.1	0.34	0.000	0.656	0.828
Cards	Runway Gen-4.5	0.03	0.000	0.750	0.992
Cards	Cosmos3-Super	0.03	0.000	0.750	0.992

Appendix

Table 7: MCAR sensitivity for the null-heavy scenes. For each cell we impute the

N-n_{\mathrm{valid}}

nulls to minimise (best) and maximise (worst) total variation over the full

N

;

\mathrm{TV}_{\mathrm{rep}}=(1-\rho)+\rho\,\mathrm{TV}(\hat{p},p_{0})

is the reported null-extended charge.

Scene	$n$	Agreement	FN	MN	WL
Physical board	18	18/18 (100%)	0/13	0/5	0
Animated board	18	17/18 (94%)	0/13	1/5	0
Ball fork	18	17/18 (94%)	0/17	0/1	1
Walking	18	17/18 (94%)	0/17	0/1	1
Pendulum	18	16/18 (89%)	2/2	0/16	0
Dice	18	18/18 (100%)	0/18	—	0

Appendix

Table 8: Validation of the VLM outcome extraction pipeline against human annotation on a stratified sample (

N=18

per environment;

162

total). FN : False-Null rate (VLM marked null , human marked valid) over human-labelled outcomes. MN : Missed-Null rate (VLM extracted an outcome, human marked null ) over human-null cases. WL : Wrong-Label cases where both annotators assigned definite outcomes but disagreed on the category. Dashes indicate a zero denominator.

Scene	480p	720p	480p	720p	480p	720p
	$\rho$		$p$		TV
Physical board	0.59	0.47	0.088	$<$ 0.001	0.275	0.327
Animated board	0.88	0.81	$<$ 0.001	$<$ 0.001	0.657	0.467
Ball fork	1.00	0.97	0.051	0.719	0.188	0.048
Walking	1.00	1.00	0.051	0.111	0.188	0.156
Pendulum	0.06	0.09	$\dagger$	$\dagger$	0.000 †	0.500 †

Appendix

Table 9: SeeDance-2.0 at its benchmarked 480p vs 720p (same frames, prompts, 32 seeds; only resolution changes).

\rho=n_{\mathrm{valid}}/32

;

p

= MC

\chi^{2}

; TV vs the scene reference. Strongly-miscalibrated scenes (

p<0.001

) are unchanged by resolution.

\dagger

\leq 3

valid generations, so no

\chi^{2}

test is reported (main-text dagger rule).

Model	Benchmark dur.	$\mathrm{mnTV}$ (benchmark)	$\mathrm{mnTV}$ ( $5\,$ s)
WAN-2.7	$3\,$ s	0.58	0.56
SeeDance-2.0	$4\,$ s	0.39	0.40
HappyHorse-1.0	$3\,$ s	0.54	0.59
Veo 3.1	$4\,$ s	0.65	—
Runway Gen-4.5	$5\,$ s	0.48	0.48
Cosmos3-Super	$\sim$ 5 s	0.63	0.63

Appendix

Table 10: Uniform 5-second duration ablation: aggregate

\mathrm{mnTV}

(lower is better) at each model’s benchmarked duration vs. a uniform

5\,

s. WAN-2.7, SeeDance-2.0 and HappyHorse-1.0 are re-generated and re-scored at

5\,

s; Runway Gen-4.5 and Cosmos3-Super are already

\sim

5 s (reused); Veo 3.1 cannot run at

5\,

s (only

\{4,6,8\}\,

s) and is shown at its benchmarked

4\,

Guidance Scale	$\rho$ $\uparrow$	$\mathrm{TV}$ $\downarrow$	$p$ value	Modal face
1.0	0.66	0.17	0.699	1
1.5	0.78	0.17	0.394	5
3.0	0.97	0.34	0.003	5
4.5	1.00	0.26	0.042	5
6.0 (default)	0.97	0.31	0.004	5
7.5	1.00	0.45	$<$ 0.001	1

Appendix

Table 11: Cosmos3-Super dice analysis at seven guidance scale values Total Variation (

\mathrm{TV}

) and

p

values characterise calibration on the valid sample against the uniform

\{1,\ldots,6\}

reference; “modal face” is the face on which the empirical distribution peaks. Note that the two lowest-

\mathrm{TV}

settings (CFG

1.0

1.5

) also have the lowest scorability

\rho

, so their

\mathrm{TV}

is computed on fewer valid generations.

Figure 14: Empirical dice distribution at each Classifier Free Guidance (CFG) value (leftmost panel: uniform reference). At the lowest guidance settings (CFG

1.0

–

1.5

) the distribution is close to uniform; as CFG increases, mass concentrates onto faces 1 and 5 and face 6 is essentially absent for CFG

\geq 3.0

. Higher guidance sharpens the collapse onto the modal faces. Note that

n_{\mathrm{valid}}

(shown per panel) falls sharply at low CFG, so the near-uniform low-CFG panels rest on fewer valid generations.

Figure 15: Per-model confusion matrices for the explicit target-face dice ablation, 5 seeds per (model, requested face). Rows index the requested face, columns index the rolled face (plus a final null column for invalid video generations). Diagonal cells (correctly-followed instruction) are outlined. Numbers in parentheses are overall compliance across all requested faces.

Model	Compliance
SeeDance-2.0	63.3%
WAN-2.7	46.4%
Veo 3.1	43.3%
Cosmos3-Super	33.3%
Runway Gen-4.5	28.6%
HappyHorse	16.7% (chance)

Appendix

Table 12: Overall compliance on the explicit target-face dice ablation. Chance compliance under no instruction-following is

1/6\approx 16.7\%

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