GeoWM: Efficient Direct World Modeling in Explicit Geometry

Mehrdad Noori; Guile Wu; Sam Hosseini; Dongfeng Bai

cs.CVOct 5, 2026

GeoWM: Efficient Direct World Modeling in Explicit Geometry

Authors: Mehrdad Noori, Guile Wu, Sam Hosseini, Dongfeng Bai

Organizations: Huawei Noah’s Ark Lab, Canada

Abstract

Modeling 3D scene geometry and its evolution over time is essential for autonomous driving and robotics. A common paradigm is to use world models to predict future images or latent representations of the environment and subsequently recover geometry from these predictions. However, this paradigm does not explicitly model geometric structure and typically relies on recursive rollouts to reach longer prediction horizons, leading to error accumulation and increasing computational cost. To address these limitations, we present GeoWM, a geometry world model that directly forecasts future scene geometry at specified future horizons without recursive rollout. The key idea is to leverage a geometry foundation model to transform observed RGB frames into a geometric history, which conditions a flow-matching transformer to predict the scene geometry at a specified future horizon. We further show that a lightweight camera-motion predictor can accurately estimate the future viewpoint, and that projecting the observed geometry into the predicted viewpoint provides an effective geometric prior for future geometry forecasting. Extensive experiments on four datasets spanning urban driving, aerial flight, and dynamic manipulation demonstrate that GeoWM outperforms the evaluated world models in forecasting depth, camera pose, and 3D scene geometry, while substantially reducing inference time at longer horizons.

Figures & tables

Fig. 1 : Pixels, features, or explicit geometry? Video models forecast future frames and then reconstruct geometry; their photometric objective couples only loosely to 3D structure, and dynamic objects can be mislocalised [ 7 ] . Feature-space models forecast latents and decode them, where decoding can amplify errors [ 7 ] and autoregressive rollout accumulates them [ 8 , 9 , 10 ] . GeoWM forecasts explicit geometry directly and queries each horizon independently.

Fig. 2 : Overview of GeoWM : (a) forecasting in explicit geometry, (b) the flow-matching transformer, and (c) independent horizon queries.

KITTI next 0.21 s, short 0.41–1.03 s, mid 1.24–2.07 s, long 2.27–4.14 s
Method	Next			Short			Mid			Long			All			Pose (trajectory-level)
Method	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	ATE $\downarrow$	RTE $\downarrow$	RRE $\downarrow$
Copy-last	9.1	90.1	0.754	13.9	82.6	0.900	18.9	75.7	1.152	22.5	71.8	1.406	19.2	75.8	1.209	6.82	1.33	0.83
DINO-Foresight	15.0	81.0	–	16.1	79.1	–	19.2	72.1	–	22.6	64.1	–	20.0	69.9	–	–	–	–
VGGT-World	7.8	92.4	0.737	11.2	87.8	0.796	21.4	73.9	1.263	29.1	57.6	2.123	22.5	69.5	1.574	3.43	1.39	1.50
Cosmos-3	6.8	93.8	0.676	9.3	90.5	0.735	15.1	83.5	0.957	21.2	75.5	1.281	16.6	81.4	1.060	0.34	0.22	0.67

TABLE I : Future geometry forecasting on four datasets. AbsRel (

\times 100

) and

\delta_{1}

(%) score the forecast depth, CD (m) the forecast 3D geometry after similarity alignment, and ATE (m), RTE (m), RRE (deg) the forecast camera trajectory. Next is the first predicted horizon; Short , Mid , and Long average the horizons given in each block, and All averages every horizon. Depth is median-scaled per image except on DOMINO, which is evaluated at true scale. Best and second best among copy-last, VGGT-World [ 7 ] , Cosmos-3 [ 6 ] , and GeoWM ; copy-last repeats the last observed geometry.

DOMINO, novel task
Method	Next			Short			Mid			Long			All
Method	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	CD $\downarrow$
Copy-last	14.1	85.4	0.032	16.0	83.1	0.039	22.6	77.6	0.055	30.9	71.6	0.075	21.9	78.6	0.053
VGGT-World	16.0	84.1	0.040	18.7	81.1	0.050	27.4	73.6	0.071	32.3	65.9	0.079	24.7	75.0	0.063
Cosmos-3	15.1	85.9	0.038	16.6	84.1	0.044	22.3	78.8	0.059	27.9	73.3	0.075	21.2	79.7	0.057
GeoWM	5.1	93.7	0.017	7.4	90.3	0.026	14.7	81.1	0.048	23.4	71.8	0.071	13.7	82.9	0.044

TABLE II : Generalisation on DOMINO to unseen tasks and robots. Same metrics, horizon groups, and ranking as the DOMINO block of Table I , which reports the seen tasks and robots.

Prediction space
Variant	Short		Long		All
Variant	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$
Copy-last	13.9	82.6	22.5	71.8	19.2	75.8
feature space	11.7	86.6	21.4	72.8	17.6	78.1
feature space, + depth loss	11.8	86.6	18.8	73.7	16.0	78.8
Geometric conditioning

TABLE III : Ablations on KITTI. Variants of GeoWM , evaluated on the windows and with the protocol of Table I : median-scaled AbsRel (

\times 100

) and

\delta_{1}

(%), averaged over the KITTI horizon groups of that table, where All averages every horizon.

N

is the number of noise draws averaged at read-out.

Fig. 3 : Direct forecasting and geometric conditioning. (a) Direct prediction versus one-step recursive rollout with the same checkpoint. (b) Increase in horizon-averaged AbsRel when scaling the anchor’s predicted translation relative to

\alpha=1

; rotation is unchanged. Comparisons use matched window subsets and equal-drive averaging on KITTI.

Fig. 4 : Qualitative forecasts. Short/long horizons are $h=1/10$ for TartanAir and $h=4/48$ for DOMINO. Error maps show signed relative depth error (white is zero); boxes mark corresponding scene regions. Clouds use calibrated intrinsics, median-scaled TartanAir depths and fixed-scale DOMINO depths; colors indicate depth. All clouds share the same view without further alignment.

Method	TFLOPs	Params			Time to forecast (s)
Method	TFLOPs	forecaster	backbone	total	$h{=}1$	$h{=}5$	$h{=}10$	$h{=}20$
DINO-Foresight [ 5 ]	30.6	256 M	DINO	361 M	0.03	0.11	0.22	0.42
VGGT-World [ 7 ]	1116	433 M	VGGT	1.59 B	1.9	7.7	17.4	36.9
Cosmos-3 [ 6 ]	3362	17.0 B	VGGT	18.1 B	4.9	5.8	6.7	9.3
GeoWM	12.0	206 M	VGGT	1.36 B	0.11	0.11	0.11	0.11

TABLE IV : Inference cost. Compute, parameters and the time to obtain the forecasts of different horizons.

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GeoWAM: Visual Geometry World Action Models for Autonomous Driving

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Autonomous Driving World Models Geogs-Slam Ego-Trajectory Prediction Goal-Conditioned Dynamic Manipulation

Open paper AskPDF arXiv

World action models (WAMs) have recently gained increasing attention as a framework for jointly modeling scene evolution and ego actions in autonomous driving. Most existing WAMs learn scene dynamics in pixel space by combining a video-generation backbone for future-observation prediction with an action head for ego-trajectory prediction. Pixels, however, provide only an indirect representation of these dynamics: they entangle geometry and motion with appearance, texture, and illumination, forcing the model to infer three-dimensional transformations from two-dimensional observations. We argue that point-based geometry provides a more natural state space for driving. It explicitly captures spatial structure and both rigid and non-rigid scene dynamics while remaining aligned with the 3D space of driving actions. Building on this insight, we introduce GeoWAM, a visual geometry world action model for autonomous driving. Rather than predicting future images, GeoWAM is pretrained to forecast future scene geometry, yielding representations that jointly encode spatial structure and temporal evolution. A geometry-conditioned action head then leverages these learned geometric dynamics to predict future ego-trajectories. Extensive experiments show that GeoWAM outperforms image-based alternatives, achieving a combined EPDMS of 36.6 on navhard without PDMS supervision and strong zero-shot generalization to nuScenes, with a collision rate of 0.24%. Scaling geometry pretraining with unlabeled data further improves performance, increasing the navhard score by 8.2% to 39.6 and strengthening zero-shot transfer to nuScenes, where the collision rate is reduced by 50% to 0.12%. Together, these results establish geometry as an effective state representation for autonomous driving and geometry pretraining as a general, scalable strategy for downstream planning.

Abstract

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