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G$^2$WAM: World Action Models for Efficient and Geometry Grounded Image-Goal Navigation
Ke Gui, Chenghao Shi, Ziyue Wang, Longwen Chen, Xieyuanli Chen, Huimin Lu
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Abstract
Abstract:World models capture environment dynamics and support counterfactual reasoning for planning. In image-goal navigation, where the target often lies beyond the current field of view, the agent must not only model environmental dynamics but also maintain a persistent spatial memory of the scene. Existing approaches either introduce spatial context by fine-tuning pretrained models on the target task, which underexploits their spatial priors, or rely on external 3D reconstruction, which is computationally expensive for real-world deployment. In this paper, we propose the Geometry Grounded World Action Model (G$^2$WAM) for image-goal navigation. G$^2$WAM encodes spatial cues through a learned scene-coordinate localization module that anchors the current, goal, and history frames in a common reference frame, yielding a stable and consistent spatial context that enables efficient navigation without explicit 3D reconstruction. Following the world-action-model paradigm, G$^2$WAM jointly predicts future states and actions, eliminating the need for costly cross-entropy method (CEM) style planning. In addition, G$^2$WAM operates entirely in latent space, avoiding the computational burden of pixel-level reconstruction and substantially reducing inference cost. Across four trajectory prediction benchmarks, G$^2$WAM reduces average ATE and RPE by 40.1% and 35.2%, respectively. In closed-loop navigation experiments, it improves the success rate from 54.0% to 63.0% and the success weighted by path length (SPL) from 36.4% to 59.2%, while maintaining high efficiency.
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- Source: https://arxiv.org/abs/2610.16558v1
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G2WAM: World Action Models for Efficient and Geometry Grounded Image-Goal Navigation Ke Gui, Chenghao Shi, Ziyue Wang, Longwen Chen, Xieyuanli Chen, Huimin Lu College of Intelligence Science and Technology, National University of Defense Technology, China National Key Laboratory of Equipment State Sensing and Smart Support, National University of Defense Technology, China School of Future Technology, National University of Defense Technology, China Abstract World models capture environment dynamics and support counterfactual reasoning for planning. In image-goal navigation, where the target often lies beyond the current field of view, the agent must not only model environmental dynamics but also maintain a persistent spatial memory of the scene. Existing approaches either introduce spatial context by fine-tuning pretrained models on the target task, which underexploits their spatial priors, or rely on external 3D reconstruction, which is computationally expensive for real-world deployment. In this paper, we propose the Geometry Grounded World Action Model (G2WAM) for image-goal navigation. G2WAM encodes spatial cues through a learned scene-coordinate localization module that anchors the current, goal, and history frames in a common reference frame, yielding a stable and consistent spatial context that enables efficient navigation without explicit 3D reconstruction. Following the world-action-model paradigm, G2WAM jointly predicts future states and actions, eliminating the need for costly cross-entropy method (CEM) style planning. In addition, G2WAM operates entirely in latent space, avoiding the computational burden of pixel-level reconstruction and substantially reducing inference cost. Across four trajectory prediction benchmarks, G2WAM reduces average ATE and RPE by 40.1% and 35.2%, respectively. In closed-loop navigation experiments, it improves the success rate from 54.0% to 63.0% and the success weighted by path length (SPL) from 36.4% to 59.2%, while maintaining high efficiency. 1 Introduction Image-goal navigation asks an agent to reach the location shown in a target image by using its stream of first-person observations. Recent advances have progressed from reactive end-to-end policies (Shah et al., 2023a; Sridhar et al., 2024; Shah et al., 2023b) to world-model-based approaches (Bar et al., 2025; Zhou et al., 2025; Zhang et al., 2025b; Hafner et al., 2025), in which the world model serves as a learned model of environment dynamics. Concretely, it can jointly capture navigation priors and scene memory within a single training pipeline, and support counterfactual reasoning that helps the agent solve complex long-horizon navigation tasks, including those whose targets lie beyond the current field of view. In practice, however, error accumulation over multi-step rollouts causes long-horizon imagination to degrade rapidly (Bar et al., 2025; Luan et al., 2026). Moreover, cross-entropy method (CEM) planning requires repeated forward evaluations, incurring high inference cost and latency, and the selected open-loop trajectory must still be converted into closed-loop waypoints at execution time, which introduces additional error. Existing methods attempt to explicitly inject depth information during training (Wu et al., 2026), or to bolt on external 3D reconstruction (Ren et al., 2025; Wang et al., 2026a), Gaussian-splatting (Ma et al., 2026), or latent spatial memory (Wu et al., 2025; Oshima et al., 2026; Wang et al., 2026b), so as to provide the world model with explicit spatial context that improves long-horizon and spatial consistency. Yet these methods either exploit spatial priors insufficiently or are too heavy for practical deployment. Our key insight is that, when navigating, humans do not maintain a precise geometric model of the environment (Warren, 2019; Ishikawa and Montello, 2006); instead, they rely on an egocentric, reactive representation (Wang and Spelke, 2002), which can be captured by the relative pose between the current view and the goal image. We therefore present the Geometry Grounded World Action Model (G2WAM) for image-goal navigation. G2WAM encodes environmental information into an end-to-end localization network and provides the agent with egocentric relative pose to the goal as well as the history trajectory as spatial cues. By anchoring all observation frames and the goal frame to fixed positions in space, we obtain a stable, geometrically consistent spatial context. In designing G2WAM, we paid particular attention to its efficiency for practical deployment. To this end, G2WAM adopts the world-action-model paradigm to jointly predict action chunks and latent future states, sidestepping the expensive CEM-style planning. It further keeps the entire rollout in latent space, avoiding pixel-level future reconstruction. Fig. 1 depicts the key difference between our method and existing methods based on world models and world action models. Figure 1: Navigation world model paradigms. Conventional world models plan over predicted observations, whereas world action models jointly predict observations and actions. G2WAM further leverages estimated spatial context to efficiently roll out future latents and executable actions. Our contributions can be summarized as follows: • We propose G2WAM, a novel implicit world action model for navigation that jointly predicts latent future states and executable action chunks, avoiding the costly CEM-style planning and heavy pixel-level reconstruction. • We introduce a new paradigm for spatial context aiding. Instead of reconstructing explicit geometry, we anchor the observation and goal frames in a shared end-to-end localization network, which efficiently provides a continuous, geometrically consistent spatial context over the navigation history and the relative target. • Extensive experiments demonstrate that G2WAM achieves the best overall trajectory prediction and navigation performance, reducing average ATE and RPE by 40.1% and 35.2% in trajectory prediction, and improving the success rate from 54% to 63% (a 9-point gain) and success weighted by path length (SPL) from 36.4% to 59.2% (a 22.8-point gain) in closed-loop navigation, while maintaining high efficiency. We will open-source our approach to benefit the research community. 2 Related Work 2.1 Visual Navigation Experience-based navigation uses recorded routes, demonstrations, or topological graphs to guide motion (Furgale and Barfoot, 2010; Pathak et al., 2018; Savinov et al., 2018; Shah et al., 2021a). Goal-conditioned policies instead map current and goal images directly to actions; representative methods include GNM (Shah et al., 2023a), ViNT (Shah et al., 2023b), and NoMaD (Sridhar et al., 2024). These methods do not explicitly predict future world states. Metric goal estimation provides complementary geometric guidance. PointGoal methods use localization or visual odometry (Wijmans et al., 2020; Partsey et al., 2022), while image-based localization estimates pose through feature matching or scene-coordinate regression (Sarlin et al., 2020; Brachmann et al., 2017; Jiang et al., 2025). AnyImageNav (Deng et al., 2026) uses recovered goal pose for precise navigation. Reactive policies have achieved promising results, but they lack modeling of environment dynamics, making them prone to pattern matching. Accordingly, recent state-of-the-art methods have progressed toward world-model-based approaches. 2.2 World Models and World Action Models for Navigation Navigation world models predict the consequences of actions in image or latent space. NWM (Bar et al., 2025) generates future images, whereas DINO-WM (Zhou et al., 2025), LS-NWM (Zhang et al., 2025a), and ReL-NWM (Zhang et al., 2025b) support planning with predicted visual features or latent states. World action models further couple state and action prediction. Spatial-perceiving WAM (Chen et al., 2026) jointly predicts RGB-D observations and waypoints, NavWAM (Azuma et al., 2026) models observations, goal progress, and action chunks, and WAMNav (Yang et al., 2026) jointly predicts latent dynamics and actions. G2WAM also performs joint latent state-action prediction, but introduces explicit spatial context through relative pose and causal motion conditioning. Unlike existing WAMs, it predicts metric waypoints through an implicit latent rollout without reconstructing future observations. Geometry-aware world models mainly improve spatial consistency in two ways. The first direction maintains geometry-grounded spatial memory. GEN3C (Ren et al., 2025) and EvoWorld (Wang et al., 2026a) construct explicit 3D scene presentations and reproject them into target views to condition visual generation. Other methods improve long-term consistency by organizing historical information according to scene geometry: long-term spatial memory (Wu et al., 2025) retrieves previously observed scene content, WorldPack (Oshima et al., 2026) selects and compresses observations using camera pose and field-of-view overlap, and Mirage (Wang et al., 2026b) stores depth-unprojected latent tokens in a persistent 3D cache. The second direction introduces geometric constraints without maintaining a persistent scene representation. Geometry Forcing (Wu et al., 2026) aligns intermediate generative features with geometric representations during training, while DR-NWM (Luan et al., 2026) uses future anchors and bidirectional epipolar guidance to reduce geometric drift during visual rollout. In contrast, G2WAM neither reconstructs an explicit 3D scene nor generates future images under geometric constraints. Instead, it derives spatial context from estimated poses, a lightweight metric condition for jointly rolling out latent states and executable actions. 3 Method We build G2WAM around a single design principle: efficient, geometry-grounded navigation. This principle is realized through two design choices. First, the spatial context is geometry-grounded without costly 3D reconstruction. A lightweight scene-coordinate localization module anchors the goal and observed frames in a shared scene frame, so the relative pose between the current view and the goal, together with the history motions, provides an egocentric geometric context that grounds the rollout in the target. Second, the model is efficient by construction. It adopts the world-action-model paradigm and rolls out entirely in latent space, avoiding CEM-style planning and pixel-level reconstruction. Together, an implicit world action model consumes this lightweight relative-geometry context and rolls it forward, jointly predicting latent future states and canonical waypoint increments. The overall architecture is shown in Fig. 2. We first describe the spatial context induced by scene-coordinate anchoring (Sec. 3.1), then the implicit world action model (Sec. 3.2), and finally how relative-pose and motion conditioning adapt the model to a concrete platform (Sec. 3.3). Training is described in Sec. 3.4. Figure 2: Overview of G2WAM. A learned localizer anchors the goal and observed frames in a shared scene frame to obtain the goal-relative pose and causal history motions. The goal image and pose guide joint latent and waypoint prediction, while the history motions condition the action branch. 3.1 Spatial Context via Scene-Coordinate Anchoring Our key insight is that an agent need not build an explicit geometric model of the environment to navigate. It needs a stable, geometrically consistent spatial context indicating where the goal lies relative to its history of visited locations. We obtain this by anchoring the observation history and the goal image in a shared scene coordinate through an end-to-end localization network. Concretely, the localization module estimates the current, goal, and history-frame poses in a shared scene frame, from which we compose the current-to-goal relative transformation and the consecutive motion increments. Let j I_j be the image at index j, and let ^jS∈SE(3) T_j^S (3) map its calibrated robot frame into the shared scene frame SS, where t, g, and i index the current, goal, and history frames. We first obtain each pose through a scene-specific image localization module flocf_loc: ^jS=floc(j,S),j∈t−3,…,t,g, T_j^S=f_loc( I_j;D_S), j∈\t-3,…,t,g\, (1) where SD_S denotes pre-collected scene data and camera-to-robot calibration is included in the interface. We then compute ^t→g=(^tS)−1^gS,^i→i+1=(^iS)−1^i+1S,i=t−3,…,t−1. T_t→ g=( T_t^S)^-1 T_g^S, T_i→ i+1=( T_i^S)^-1 T_i+1^S, i=t-3,…,t-1. (2) The planar translation of ^t→g T_t→ g is converted to the model’s coordinate convention and divided by the waypoint spacing ℓ to form t p_t; the consecutive transforms give the history-dependent entries of t m_t. These are embedded as tpose e_t^pose and tmotion e_t^motion (Sec. 3.3) and condition the latent rollout in Sec. 3.2. This design separates the world action model from the localization network: since the model consumes only the current-to-goal relative transformation and recent causal motion, the localization network can be any end-to-end method or a traditional place-recognition-plus-pose-estimation pipeline, without changing the architecture. This plug-and-play property makes the world action model agnostic to the localization interface. By default, we use R-SCoRe (Jiang et al., 2025), a state-of-the-art image-based end-to-end localizer that maps images to geometrically grounded correspondences for robust 6-DoF pose estimation, achieving 64.3% success within (0.25m,2∘)(0.25\,m,2 ) at 140–270 ms per query on an RTX 2080. Note that scene-coordinate anchoring assumes a previously seen scene, as it requires pre-collected trajectory data. This is practically meaningful because our method targets out-of-field-of-view navigation. In a completely unknown scene, such a task can rely only on a world model’s imagination, which is empirical and unreliable since any configuration is possible. Existing methods therefore resort to fine-tuning or external 3D reconstruction. Our method instead anchors observations and the goal to fixed spatial positions via end-to-end localization, exploiting scene information more directly than fine-tuning and more lightly than 3D reconstruction. 3.2 Implicit World Action Model The world action model is built to roll out task-relevant state without ever reconstructing an image. This choice is deliberate: navigation only requires the model to track where the agent is heading, not to reproduce the appearance of the scene, so an abstract latent rollout suffices. We therefore predict the next patch latent and the corresponding action from a shared goal-conditioned transition context, never passing through an image decoder. The relative pose t p_t and motion profile t m_t from Sec. 3.1 enter this model through their embeddings tpose e_t^pose and tmotion e_t^motion, defined in Sec. 3.3. A frozen DINOv3 encoder (Siméoni et al., 2025) maps the observation history and goal image into patch latents t−H+1:t∈ℝH×P×D z_t-H+1:t ^H× P× D and g∈ℝP×D z_g ^P× D, where H=4H=4 is the context length, P the number of patches, and D=384D=384 the latent dimension. The goal embedding is g=ϕg(pool(LN(g))) q_g= _g(pool(LN( z_g))), where ϕg _g is a two-layer MLP, LNLN is layer normalization, and poolpool denotes mean pooling over patches. At rollout step k∈0,…,7k∈\0,…,7\, the model maintains a fixed-length latent history and computes t+k c_t+k =Transition(t+k−H+1:t+k,g,tpose), =Transition\! ( z_t+k-H+1:t+k, q_g, e_t^pose ), (3) t+k s_t+k =pool(t+k)+tpose+tmotion, =pool( c_t+k)+ e_t^pose+ e_t^motion, (t+k+1,^t+kcan) ( z^J_t+k+1, a_t+k^can ) =(t+k,t+k), =J\! ( c_t+k, s_t+k ), ^t+k+1 z_t+k+1 =LN(αt+k+1+αBϕB(t+k)). =LN\! ( _J z^J_t+k+1+ _B _B( c_t+k) ). The transition module fuses the latent history with the goal and relative-pose conditions to produce the patch-level context t+k∈ℝP×D c_t+k ^P× D. Its pooled representation is combined with the pose and motion embeddings to obtain the compact step state t+k∈ℝD s_t+k ^D. The joint decoder J then predicts the next latent candidate and the canonical waypoint increment ^t+kcan=(Δx,Δy,Δθ) a^can_t+k=( x, y, θ). As defined in Eq. 3, the latent candidate is combined with a base transition and appended to the fixed-length history, yielding an autoregressive latent rollout without image decoding. Detailed transition, conditioning, and decoder architectures are provided in Appendix A. 3.3 Spatial Context Conditioning And Action Adaption The two conditioning signals play distinct roles: the relative pose supplies target geometry, while the motion profile records the past trajectory and specifies how the canonical prediction is converted into executable motion. The relative-pose conditioner receives t=(Δxtg,Δytg,sinΔθtg,cosΔθtg) p_t=( x_t^g, y_t^g, _t^g, _t^g). This four-dimensional vector is derived from ^t→g T_t→ g in Eq. 2. Here Δxtg x_t^g and Δytg y_t^g are the current-to-goal planar translation in the model’s coordinate convention and in waypoint units, while Δθtg _t^g is the relative yaw. The conditioner separates translation from rotation and computes tpose=ϕfuse([ϕtrans(t,log(1+dt)),ϕyaw(t)]), e_t^pose= _fuse\! ( [ _trans\! ( u_t, (1+d_t) ), _yaw( v_t) ] ), (4) where t=(Δxtg,Δytg)/max(dt,ϵ) u_t=( x_t^g, y_t^g)/ (d_t,ε) is the normalized goal-direction vector, dt=(Δxtg)2+(Δytg)2d_t= ( x_t^g)^2+( y_t^g)^2 is the goal distance in waypoint units, t=(sinΔθtg,cosΔθtg) v_t=( _t^g, _t^g) is the relative-yaw vector, and ϵ>0ε>0 prevents division by zero. The brackets denote concatenation. The functions ϕtrans _trans and ϕyaw _yaw are separate two-layer MLPs. The fusion function ϕfuse _fuse applies a two-layer MLP followed by layer normalization. Independently, the motion conditioner receives the five-dimensional profile formed from the consecutive transforms in Eq. 2, t=[d¯t,θ¯t,ds,θs,ℓ] m_t=[ d_t, θ_t,d_s, _s, ] T. The history-dependent terms are the median per-step distance d¯t d_t, divided by waypoint spacing ℓ , and the mean absolute per-step yaw change θ¯t θ_t. The dataset-level translation and yaw scales are dsd_s and θs _s, respectively; ℓ is the waypoint spacing in metres. A two-layer MLP with layer normalization maps this profile to the motion embedding tmotion=ϕmotion(log(+t)) e_t^motion= _motion( ( 1+ m_t)), where the logarithm is applied componentwise. A canonical-motion adapter A maps each canonical prediction to the action interface: ^t+k=A(^t+kcan,t)=[xy(d~t^t+k,xycan);θ~sa^θ,t+kcan]. a_t+k=A\! ( a_t+k^can, m_t )= [N_xy\! ( d_t a_t+k,xy^can ); θ_s a_θ,t+k^can ]. (5) Here ^t+k,xycan a_t+k,xy^can denotes the two-dimensional canonical translation, a^θ,t+kcan a_θ,t+k^can the scalar canonical yaw, d~t=clip(d¯t,0.1,4.0) d_t=clip( d_t,0.1,4.0), and θ~s=clip(θs,0.05,1.0) θ_s=clip( _s,0.05,1.0). The semicolon denotes concatenation. For a two-dimensional input ξ, the planar normalization is xy()=2(−min)⊘(max−min)−N_xy( ξ)=2( ξ- b_ ) ( b_ - b_ )- 1, where min b_ and max b_ are fixed two-dimensional action bounds, ⊘ denotes componentwise division, and 1 is the two-dimensional all-ones vector. This function maps translation in waypoint units to the normalized planar action interface. Thus t p_t supplies target geometry, whereas t m_t specifies how the canonical prediction is converted into platform-specific motion. 3.4 Training We train the G2WAM end-to-end with a multi-term objective, while the localization interface is trained separately. The latent loss combines a cosine term and a small mean-squared-error term, the action loss is a smooth-ℓ1 _1 on the canonical action, and trajectory supervision compares cumulative waypoint coordinates and yaw over the rollout. Rare turns receive extra weight so the model does not collapse to always-advance behavior: ℒ=λzℒz+λaℒa+λtrajℒtraj+λyawℒyaw,L= _zL_z+ _aL_a+ _trajL_traj+ _yawL_yaw, (6) The two direct prediction terms are ℒz _z =1−Cos(^,∗)+0.3MSE(^,∗), =1-Cos( Z, Z^*)+0.3MSE( Z, Z^*), (7) ℒa _a =∑b,kwb,kℓSL1(^b,t+kcan,b,t+kcan,∗)∑b,kwb,k, = _b,kw_b,k\, _SL1( a^can_b,t+k, a^can,*_b,t+k) _b,kw_b,k, where Z and ∗ Z^* stack the predicted and target patch latents across rollout steps, CosCos averages patchwise cosine similarity, MSEMSE averages squared feature error, and ℓSL1 _SL1 averages smooth-ℓ1 _1 error over the three canonical-action components. The weight wb,kw_b,k increases for turning steps according to the target executable yaw increment and applies to the entire action increment. The remaining terms ℒtrajL_traj and ℒyawL_yaw compare cumulative executable waypoint positions and yaw using ℓ1 _1 losses, with planar increments unnormalized before accumulation. The scalar coefficients λz,λa,λtraj,λyaw _z, _a, _traj, _yaw weight these four losses, whose values are 0.30.3, 3.03.0, 2.02.0, and 0.50.5, respectively. We use AdamW with batch size 3232, zero weight decay, and gradient-norm clipping at 1010. 4 Experiments We conduct our experiments to show that G2WAM (i) achieves state-of-the-art trajectory prediction and, with a stronger localization method, holds sufficiently high potential for even better prediction; (i) retains performance comparable to the baselines even when transferred zero-shot to a new scene where the spatial context is lost; (i) performs effective closed-loop navigation; (iv) benefits substantially from the proposed spatial-context mechanism; and (v) attains state-of-the-art performance together with high runtime efficiency. We first describe the setup, then address each claim in turn. 4.1 Experimental Setup Datasets. We evaluate 8-step trajectory prediction on RECON (Shah et al., 2021b), SACSoN (Hirose et al., 2024), TartanDrive (Triest et al., 2022), and SCAND (Karnan et al., 2022), using 100 fixed test queries per dataset shared across methods, following Bar et al. (2025). We further evaluate zero-shot transfer to Go Stanford (Hirose et al., 2019). For closed-loop ImageGoal navigation, we use 100 fixed Gibson (Xia et al., 2018) validation episodes from the known Mosquito scene in Habitat-Sim (Savva et al., 2019). These episodes are disjoint from the same-scene trajectories used to fine-tune the navigation model and train the localization interface. We also present a variant of our approach that uses the ground-truth pose to provide spatial context, denoted as G2WAM-GT, to show how much our method can benefit from an ideal spatial context. Baselines. The trajectory comparison includes direct navigation policies GNM (Shah et al., 2023a) and NoMaD (Sridhar et al., 2024), predictive world models NWM (Bar et al., 2025), DINO-WM (Zhou et al., 2025), DreamerV3 (Hafner et al., 2025), LeWM (Maes et al., 2026), and LS-NWM (Zhang et al., 2025a), and geometry-aware models EvoWorld (Wang et al., 2026a) and Geometry Forcing (Wu et al., 2026). Each comparison uses identical held-out queries or episodes and the same metric definitions, while methods retain their own prediction and action-selection procedures. Trainable methods use the corresponding benchmark’s training trajectories for adaptation. Spatial-perceiving WAM (Chen et al., 2026), NavWAM (Azuma et al., 2026), and WAM-Nav (Yang et al., 2026) are not quantitatively compared because their official implementations were unavailable at the time of submission. Metrics. For trajectory prediction, we report absolute trajectory error (ATE), the mean Euclidean distance between predicted and ground-truth terminal positions after eight steps, and relative pose error (RPE), the mean per-step Euclidean error between predicted and ground-truth waypoint increments. For navigation, we report For navigation, we report success rate (SR), success weighted by path length (SPL), and final geodesic distance to goal (DTG). Each episode executes at least one action, after which the evaluator issues STOP when the geodesic distance falls below 2 m, following (Zhang et al., 2025a). For inference efficiency, we measure single-step and 16-step rollout latency on an H800 using bfloat16 and batch size 16. 4.2 Trajectory Prediction This experiment tests claims (i) and (i) in the prediction setting. As shown in Table 1, G2WAM quantitatively attains the best average ATE/RPE of 1.82/0.461.82/0.46 across the four datasets, substantially reducing ATE/RPE by 40.1%/35.2%40.1\%/35.2\% relative to the second-best baseline. The improvement is most pronounced on SACSoN and TartanDrive, which we attribute to the reliable spatial and motion conditions in SACSoN and the diverse motion scales in TartanDrive. In addition, our method performs comparably to the baselines on RECON but degrades on SCAND, mainly because cross-platform motion, operator variation, and dynamic pedestrians severely limit localization performance, thereby undermining the gains it provides to the world model. Note that, when using ground-truth pose, G2WAM-GT achieves a substantial performance gain. This gain indicates that our method holds high potential when provided with a better spatial context. Table 1: 8-step trajectory prediction. Bold denotes the best and underlined the second-best value among non-GT methods. Method RECON SACSoN TartanDrive SCAND Average GNM (Shah et al., 2023a) 1.87/0.73 3.71/1.00 6.65/1.62 2.12/1.61 3.59/1.24 NoMaD (Sridhar et al., 2024) 1.95/0.53 3.73/0.96 6.32/1.31 2.24/0.49 3.56/0.82 NWM (Bar et al., 2025) 1.13/0.35 4.12/0.96 5.63/1.18 1.28/0.33 3.04/0.71 DINO-WM (Zhou et al., 2025) 2.33/0.54 5.39/1.10 5.00/1.06 1.87/0.42 3.65/0.78 DreamerV3 (Hafner et al., 2025) 1.88/0.34 4.86/1.01 5.96/1.24 1.38/0.34 3.52/0.73 LeWM (Maes et al., 2026) 2.20/0.66 4.01/1.05 4.93/1.31 2.16/0.58 3.33/0.90 LS-NWM (Zhang et al., 2025a) 1.60/0.42 4.29/0.99 5.50/1.28 1.26/0.33 3.16/0.76 EvoWorld (Wang et al., 2026a) 3.10/0.72 5.86/1.22 6.55/1.35 2.95/0.63 4.61/0.98 Geometry Forcing (Wu et al., 2026) 1.64/0.48 4.47/0.94 5.23/1.11 1.15/0.31 3.13/0.71 G2WAM 1.38/0.36 1.18/0.40 2.70/0.63 2.04/0.45 1.82/0.46 G2WAM-GT 0.46/0.18 0.94/0.35 1.13/0.36 0.57/0.23 0.78/0.28 Figure 3: 8-step trajectory rollouts on RECON, SACSoN, TartanDrive, and SCAND, with all paths aligned at the rollout origin. The qualitative rollouts in Fig. 3 illustrate the same trend. Baseline trajectories often drift away from the target direction or accumulate scale error over the 8-step horizon, whereas G2WAM rollouts remain better aligned with the ground-truth path. G2WAM-GT yields the cleanest rollouts, and G2WAM preserves much of this structure under an image-based pose interface. These results support the main design choice of predicting canonical waypoint increments directly from a goal-conditioned latent transition, rather than relying on a separate sampling or trajectory-selection stage. Table 3 evaluates our method when zero-shot transferred to a new scene without spatial context. Though not the primary scenario of this paper, this setting tests whether our world action model backbone has learned generalizable navigation priors without spatial context. We also report results with a localization module trained on a subset of the dataset, referred to as G2WAM-PoseFT, and with ground-truth pose simulating external localization devices such as GPS or UWM. Without spatial context, our method performs comparably to the baselines, indicating that our WAM does not rely solely on spatial context but possesses certain navigation priors. With pose assistance, it improves ATE/RPE by 14.0%/16.5%. 4.3 Closed-Loop Navigation Table 2: Zero-shot trajectory prediction on Go Stanford. Bold denotes the best result and underlining the second-best result. Method ATE ↓ RPE ↓ NWM (Bar et al., 2025) 2.3535 0.6447 DINO-WM (Zhou et al., 2025) 2.8993 0.7275 LeWM (Maes et al., 2026) 3.0258 0.7602 Geometry Forcing (Wu et al., 2026) 2.0981 0.6063 G2WAM 2.3096 0.6510 G2WAM-PoseFT 1.9866 0.5434 G2WAM-GT 1.5424 0.4296 Table 3: Gibson image goal navigation. Bold denotes the best result and underlining the second-best result. Method SR ↑ SPL ↑ DTG ↓ GNM (Shah et al., 2023a) 24.0% 22.8% 5.37 NoMaD (Sridhar et al., 2024) 28.0% 27.4% 4.78 NWM (Bar et al., 2025) 32.0% 26.35% 5.39 DINO-WM (Zhou et al., 2025) 54.0% 36.4% 4.56 DreamerV3 (Hafner et al., 2025) 44.0% 33.7% 5.04 LeWM (Maes et al., 2026) 42.0% 33.01% 4.51 G2WAM 63.0% 59.2% 3.39 G2WAM-GT 71.0% 70.0% 3.04 This experiment tests claim (i) in the closed-loop navigation. Concretely, it tests whether the predicted waypoints remain useful after their execution changes the observation and the estimated spatial context, rather than only achieving low open-loop trajectory error. Table 3 shows that G2WAM achieves 63.0% SR, 59.2% SPL, and 3.39 m final DTG. Compared with DINO-WM, the strongest baseline, it improves the two metrics by 9.0 and 22.8 percentage points, respectively. Its final DTG is also 25% lower than that of LeWM, the strongest baseline on this metric. The improvements across all three measures show that the waypoint predictions remain effective when executed in a repeated observe-and-replan loop, not only in open-loop trajectory prediction. The larger SPL gain over the baselines indicates that, aided by spatial context, our method navigates more purposefully and thus more efficiently. G2WAM-GT reaches 71.0% SR, 70.0% SPL, and 3.04 m final DTG. The gaps to G2WAM indicate that our method still leaves considerable room for improvement. Figure 5 shows the navigation success rate under different initial start-to-goal distances. The results indicate that spatial context plays a substantial role in both short- and long-range navigation. For long-range navigation, our spatial context does not yield a larger gap over the baselines, possibly because longer distances offer more opportunities for complex structured obstacles to appear between the current position and the goal, which makes direct goal-directed guidance insufficient. 4.4 Ablations Table 4: Conditioning ablation under the 8-step trajectory-prediction protocol. Dataset Pose + motion Pose only None GT+GT Pred.+GT Pred.+Pred. GT Pred. RECON 0.46/0.18 1.17/0.33 1.38/0.36 0.77/0.33 1.38/0.37 2.02/0.58 SACSoN 0.94/0.35 1.15/0.39 1.18/0.40 1.42/0.48 1.42/0.46 2.32/0.62 TartanDrive 1.13/0.36 1.70/0.48 2.70/0.63 3.56/0.96 4.53/0.93 5.64/1.19 SCAND 0.57/0.23 1.55/0.38 2.04/0.45 0.78/0.29 1.96/0.44 1.96/0.47 Average 0.78/0.28 1.39/0.39 1.82/0.46 1.63/0.52 2.32/0.55 2.99/0.71 This section tests claim (iv): the proposed spatial-context mechanism markedly improves navigation. We ablate the spatial conditions to assess whether goal-relative pose and causal motion provide complementary information for trajectory prediction. We evaluate the method under different conditioning settings, as in Table 4. The variant without any spatial context is denoted as None; the variant that provides only the goal and current-image poses is denoted as Pose only; and the variant that additionally provides the goal, current, and history trajectories is denoted as Pose+motion. For Pose+motion, we test three combinations using either ground-truth or R-SCoRe-estimated poses, where, e.g., GT+GT indicates that both pose and motion use ground truth. The results show that both inputs are necessary. With the current state-of-the-art R-SCoRe pipeline, pose and motion yield average gains of 39.1%/35.2% on ATE/RPE, respectively, and with ideal pose estimation or external localization these gains can expand to 73.9%/60.6%. Table 5: Runtime analysis on an NVIDIA H800 PCIe GPU. Step and 16-step are model-side timings. Type Method 1-step (ms) ↓ 16-step (ms) ↓ Action selection (s) ↓ L-WM DreamerV3 9 33 0.65 LeWM 2 34 0.36 DINO-WM 26 423 14.45 I-WM NWM 705 11430 10.98 Geometry Forcing 23486 47227 541.23 G-WM EvoWorld 7048 91175 150.26 G-WAM G2WAM 4 47 0.51 Figure 4: Closed-loop success rate grouped by initial geodesic distance. n denotes the number of episodes in each distance range. 4.5 Runtime Analysis To assess the high computational efficiency of our approach as claimed in (v), we compare inference latency under a 16-step rollout and action-selection protocol, as shown in Table 5. We annotate each method with its type: V-WM denotes a video world model, L-WM a latent world model that rolls out in latent space, G-WM a geometry-aware world model, and G-WAM a geometry-aware world-action model. No world action model methods are included, since the relevant works Chen et al. (2026); Azuma et al. (2026); Yang et al. (2026) are not open-sourced. World-model-based methods generally take longer because they must perform CEM planning. Our method is comparable in efficiency to state-of-the-art L-WM methods and has a clear advantage in action selection. We further analyze the runtime breakdown of action selection. Our method’s runtime mainly consists of localization time and world action model inference time, where localization takes 0.42 s, which also offers a clear advantage over EvoWorld’s geometric-context encoding time of 0.57 s. EvoWorld’s overall action-selection cost reaches 8.78.7 s, since it re-encodes the geometric context at every CEM rollout. 5 Conclusion We presented G2WAM, a geometry-grounded world action model for image-goal navigation. G2WAM encodes spatial cues through a learned end-to-end localization module that anchors the goal and observed frames in a common reference frame, yielding a stable and consistent spatial context that enables efficient navigation without explicit 3D reconstruction. 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Lu Efficient image-goal navigation with representative latent world model. arXiv preprint arXiv:2511.11011. Cited by: §1, §2.2. Zhou et al. (2025) G. Zhou, H. Pan, Y. LeCun, and L. Pinto DINO-WM: world models on pre-trained visual features enable zero-shot planning. In Proc. Int. Conf. Mach. Learn. (ICML), Proceedings of Machine Learning Research, Vol. 267, p. 79115–79135. Cited by: §1, §2.2, §4.1, Table 1, Table 3, Table 3. Appendix A Implementation Details A.1 World-Action Model Architecture Visual encoding. All current, historical, and goal images are resized to 224×224224× 224 before being passed through a frozen DINOv3 encoder (Siméoni et al., 2025). The encoder produces patch-level features with latent dimension D=384D=384. We retain the patch structure rather than spatially pooling the observation features, because the transition model uses patch-level information to represent spatial changes across observations. At planning step t, the model receives the four most recent observation latents, t−3:t∈ℝ4×P×D z_t-3:t ^4× P× D, and the goal-image latent g∈ℝP×D z_g ^P× D. The goal latent is first layer-normalized and then mean-pooled over its P patches. A two-layer MLP with a GELU activation maps the pooled feature into the goal embedding: g=ϕg(pool(LN(g))). q_g= _g (pool (LN( z_g) ) ). (8) The DINOv3 encoder remains frozen during world-action-model training, while the goal projection, transition module, conditioners, joint decoder, and output heads are optimized. Relative-pose embedding. The relative-pose conditioner receives t=(Δxtg,Δytg,sinΔθtg,cosΔθtg), p_t= ( x_t^g, y_t^g, _t^g, _t^g ), (9) where the planar translation is expressed in the current robot frame and divided by the dataset waypoint spacing. The implementation separates the translation and yaw components before embedding them. Let dt=(Δxtg)2+(Δytg)2,t=(Δxtg,Δytg)max(dt,ϵ),d_t= ( x_t^g)^2+( y_t^g)^2, u_t= ( x_t^g, y_t^g) (d_t,ε), (10) where t u_t is the normalized goal direction and ϵε prevents division by zero. The translation branch receives [t,log(1+dt)][ u_t, (1+d_t)], while the yaw branch receives (sinΔθtg,cosΔθtg)( _t^g, _t^g). Each branch is a two-layer MLP with a GELU activation. Their outputs are concatenated and passed through another two-layer MLP followed by layer normalization: tpose=ϕfuse([ϕtrans(t,log(1+dt));ϕyaw(sinΔθtg,cosΔθtg)]). e_t^pose= _fuse ( [ _trans ( u_t, (1+d_t) ); _yaw ( _t^g, _t^g ) ] ). (11) This decomposition preserves goal direction, logarithmic distance, and relative yaw rather than treating the four-dimensional pose condition as an unstructured vector. Causal-motion embedding. The motion conditioner receives the five-dimensional profile t=[d¯t,θ¯t,ds,θs,ℓ], m_t= [ d_t, θ_t,d_s, _s, ] T, (12) where d¯t d_t and θ¯t θ_t summarize recent estimated translation and rotation, dsd_s and θs _s are dataset-level translation and yaw scales, and ℓ is the waypoint spacing in metres. All entries are nonnegative. The implementation applies a componentwise log(1+x) (1+x) transform before passing the profile through a two-layer MLP with a GELU activation and layer normalization: tmotion=ϕmotion(log(+t)). e_t^motion= _motion ( ( 1+ m_t) ). (13) The logarithmic transform reduces the effect of scale differences between datasets and platforms. Spatiotemporal latent transition. The four-frame latent history is first layer-normalized and reshaped from ℝH×P×DR^H× P× D into a sequence containing HPHP patch tokens. Learned temporal and patch positional embeddings are added to each token: i,p=LN(i,p)+itime+ppatch, x_i,p=LN( z_i,p)+ e_i^time+ e_p^patch, (14) where i indexes the history frame and p indexes the patch. Projected goal and relative-pose embeddings are then added to every spatiotemporal token: ~i,p=i,p+ϕg→tok(g)+ϕp→tok(tpose). x_i,p= x_i,p+ _g ( q_g)+ _p ( e_t^pose). (15) A token-selection module compresses the full spatiotemporal sequence into eight learned tokens. Concretely, it predicts a normalized attention map over all HPHP input patches for each learned token and uses the resulting attention weights to compute weighted sums of the input features. The eight selected tokens therefore summarize the four-frame latent history while retaining information from all spatial locations. The goal and relative-pose projections are added again to the learned tokens before they enter a four-layer Transformer encoder. Each Transformer layer uses eight attention heads and a feed-forward dimension of 4D4D. The encoded tokens are subsequently fused back into the original spatiotemporal patch sequence through a learned token-to-patch mixing module. This operation produces a fused feature for every patch in every history frame rather than returning only a small set of global tokens. The fused patches corresponding to the latest observation are used as queries in an eight-head cross-attention operation. The complete fused spatiotemporal sequence serves as keys and values: t+k=MHA(last,fused,fused). h_t+k=MHA ( x^last, x^fused, x^fused ). (16) The attended features are combined with the latest-frame patches, a projected goal bias, and a projected relative-pose bias: t+k=LN(t+k+last+ϕg→next(g)+ϕp→next(tpose)). c_t+k=LN ( h_t+k+ x^last+ _g ( q_g)+ _p ( e_t^pose) ). (17) The resulting t+k∈ℝP×D c_t+k ^P× D is the patch-level transition context used by both latent-state and action prediction. The relative-pose embedding is therefore injected at four locations: the full patch sequence, the learned-token sequence, the cross-attention residual, and the pooled step state. The causal-motion embedding is injected only into the pooled step state. This asymmetry lets the relative pose constrain the spatial evolution of the latent representation, while recent motion and platform scale primarily affect action generation. Joint latent–action decoder. The patch-level context is mean-pooled and combined with the pose and motion embeddings: t+k=pool(t+k)+tpose+tmotion. s_t+k=pool( c_t+k)+ e_t^pose+ e_t^motion. (18) This produces a compact t+k∈ℝD s_t+k ^D step representation for control. The joint decoder contains learned action and state-summary query tokens. The shared step representation is added to both queries. Patch-level latent tokens are formed by adding a learned latent-type embedding to t+k c_t+k. Action, state-summary, and latent-type embeddings distinguish the three token streams. The resulting token sequence is processed by a two-layer Transformer encoder with eight attention heads, pre-normalization, GELU activations, and a feed-forward dimension of 4D4D. Separate linear heads read the transformed action query and latent patch tokens. The action head produces the canonical waypoint increment ^t+kcan=(Δxt+k,Δyt+k,Δθt+k), a^can_t+k= ( x_t+k, y_t+k, _t+k ), (19) while the latent head produces the patchwise candidate t+k+1 z^J_t+k+1. The implementation also retains an internal state-summary output from the state query, while the recurrent latent update and executable action are determined by the latent and action outputs. Residual latent update. In parallel with the joint decoder, a linear base projection produces t+k+1B=ϕB(t+k). z^B_t+k+1= _B( c_t+k). (20) The final next-step latent combines the joint-decoder prediction and the base projection: ^t+k+1=LN(αt+k+1+αBt+k+1B), z_t+k+1=LN ( _J z^J_t+k+1+ _B z^B_t+k+1 ), (21) where α=1.0 _J=1.0 and αB=0.1 _B=0.1. The base branch provides a direct patch-level transition, while the joint branch supplies the dominant state-action prediction. The predicted latent is appended to the fixed-length history and the oldest latent is removed: t+k−H+2:t+k+1=[t+k−H+2:t+k;^t+k+1]. z_t+k-H+2:t+k+1= [ z_t+k-H+2:t+k; z_t+k+1 ]. (22) The model repeats this procedure autoregressively for eight rollout steps. Goal, pose, and motion conditions remain fixed within one rollout and are recomputed after the next observation in the closed-loop navigation cycle. No future RGB image is reconstructed at any rollout step. Canonical-motion adaptation. The joint decoder predicts waypoint increments in a canonical motion space. The canonical-motion adapter converts these predictions into the normalized action interface used by each dataset or platform. The planar components are multiplied by the recent translation scale, while the yaw component is multiplied by the dataset-level yaw scale: t+k,xyraw=d~t^t+k,xycan,aθ,t+kraw=θ~sa^θ,t+kcan, a^raw_t+k,xy= d_t a^can_t+k,xy, a^raw_θ,t+k= θ_s a^can_θ,t+k, (23) where d~t=clip(d¯t,0.1,4.0),θ~s=clip(θs,0.05,1.0). d_t=clip( d_t,0.1,4.0), θ_s=clip( _s,0.05,1.0). (24) The scaled planar action is normalized using fixed bounds min=(−2.5,−4.0) b_ =(-2.5,-4.0) and max=(5.0,4.0) b_ =(5.0,4.0): xy()=2−minmax−min−.N_xy( ξ)=2 ξ- b_ b_ - b_ - 1. (25) The final action output is ^t+k=[xy(d~t^t+k,xycan);θ~sa^θ,t+kcan]. a_t+k= [N_xy ( d_t a^can_t+k,xy ); θ_s a^can_θ,t+k ]. (26) The relative pose thus supplies target geometry, while the motion profile determines how a canonical waypoint is converted into dataset- or platform-specific executable motion. A.2 Training Details Training objective. The localization interface is trained separately from the world-action model. The world-action model is optimized using the multi-term objective in Eq. 6. The latent loss combines patchwise cosine distance with a smaller mean-squared-error term: ℒz=1−Cos(^,∗)+0.3MSE(^,∗).L_z=1-Cos ( Z, Z^* )+0.3MSE ( Z, Z^* ). (27) The action loss applies a smooth-ℓ1 _1 loss to the canonical translation and yaw increments. Turning steps receive larger weights to discourage collapse to an always-forward prediction: ℒa=∑b,kwb,kℓSL1(^b,t+kcan,b,t+kcan,∗)∑b,kwb,k.L_a= _b,kw_b,k _SL1 ( a^can_b,t+k, a^can,*_b,t+k ) _b,kw_b,k. (28) The trajectory and yaw losses compare cumulative executable translations and rotations over the complete rollout. Planar action increments are converted back from their normalized representation before accumulation. The loss coefficients are λz=0.3,λa=3.0,λtraj=2.0,λyaw=0.5. _z=0.3, _a=3.0, _traj=2.0, _yaw=0.5. (29) Optimization settings. We use AdamW with batch size 32, zero weight decay, and gradient-norm clipping at 10. The four-dataset checkpoint is trained for 25,800 parameter updates. It is subsequently adapted to Gibson using a mixture of expert, long-goal imitation, and recovery trajectories with a learning rate of 5×10−65× 10^-6. For the reported Mosquito closed-loop experiment, this Gibson-adapted checkpoint is further fine-tuned for 500 optimization steps on 200 Mosquito trajectories using a learning rate of 2×10−62× 10^-6. These 200 trajectories are disjoint from the fixed 100 evaluation episodes. They are also used as the reference observations for constructing the scene-specific localization database; consequently, the experiment follows a known-scene but held-out-trajectory protocol. No evaluation episode is used for world-action-model fine-tuning or localization training. The DINOv3 encoder remains frozen throughout training and fine-tuning. The localization interface is trained independently and is not updated by the world-action-model losses. At inference time, it supplies only the relative-pose and causal-motion conditions. A.3 Localization Interface R-SCoRe localization. The main text defines flocf_loc as an interface that maps an image to a pose in the shared scene frame (Eq. 1). We instantiate this interface with R-SCoRe (Jiang et al., 2025), a learned scene-coordinate localization method. R-SCoRe does not directly regress the final camera pose. Instead, it combines local image descriptors with retrieved global scene encodings to predict three-dimensional scene coordinates for query keypoints. A geometric PnP–RANSAC solver then recovers the camera pose from the resulting 2D–3D correspondences. The original R-SCoRe evaluation reports a 64.3%64.3\% localization success rate within (0.25m,2∘)(0.25\,m,2 ) and an inference time of approximately 140140–270270 ms per query on an RTX 2080. These values describe the localization benchmarks and hardware used in the original R-SCoRe evaluation, rather than the runtime of our Habitat implementation. The model-side latency reported in the main paper excludes localization, simulation, and action execution. Reference-view retrieval. For a query image j I_j, NetVLAD produces a global descriptor and retrieves a set of candidate reference views from the scene database SD_S: ℋj=RetrieveK(NetVLAD(j),S).H_j=Retrieve_K (NetVLAD( I_j),D_S ). (30) The Habitat implementation uses product-quantized nearest-neighbor search over the stored NetVLAD descriptors. The retrieved view index r∈ℋjr _j selects a candidate-specific global scene encoding r g_r from the R-SCoRe reference database. The NetVLAD descriptor is used only to retrieve candidate views. It is distinct from the global scene encoding r g_r used by the scene-coordinate prediction network. Scene-coordinate prediction. A local feature encoder extracts query keypoints u and their descriptors j, d_j, u. For each candidate reference view r, its global scene encoding is concatenated with every local query descriptor. The scene-coordinate head then predicts a three-dimensional scene coordinate: ^j,(r)=fSCR([j,;r]). X_j, u^(r)=f_SCR ([ d_j, u; g_r] ). (31) Because the global encoding is candidate-dependent, the same query keypoint produces one scene-coordinate hypothesis for every retrieved candidate. This allows the localization system to evaluate multiple possible regions of the known scene. Pose estimation and candidate selection. A separate PnP–RANSAC pose hypothesis is estimated for every retrieved candidate: (^Cj←S(r),ℐj(r))=PnP−RANSAC((,^j,(r)),j), ( T_C_j ^(r),I_j^(r) )=PnP\!-\!RANSAC (\( u, X_j, u^(r))\_ u, K_j ), (32) where j K_j is the query-camera intrinsic matrix and ℐj(r)I_j^(r) is the corresponding RANSAC inlier set. The selected candidate is r∗=argmaxr∈ℋj|ℐj(r)|.r^*= r _j |I_j^(r) |. (33) Thus, candidate selection is based on geometric consistency rather than retrieval similarity alone. The PnP solver returns a scene-to-camera pose. We invert it to obtain the camera-to-scene pose and then apply the known camera-to-robot extrinsic calibration: ^BjS=^CjS(B←C)−1. T^S_B_j= T^S_C_j ( T_B← C )^-1. (34) The resulting calibrated robot pose is the ^jS T^S_j used in Eq. 1. Shared-frame spatial context. The current, goal, and history images are independently localized in the same scene frame. Their relative transformations therefore provide the goal-relative pose and consecutive history motions: ^t→g=(^tS)−1^gS,^i→i+1=(^iS)−1^i+1S. T_t→ g= ( T^S_t )^-1 T^S_g, T_i→ i+1= ( T^S_i )^-1 T^S_i+1. (35) These relative transformations are invariant to a common rigid transformation of the shared scene frame: (^tS)−1(^gS)=(^tS)−1^gS, ( G T^S_t )^-1 ( G T^S_g )= ( T^S_t )^-1 T^S_g, (36) for any ∈SE(3) G (3). The world-action model is therefore independent of the arbitrary global origin and orientation chosen for the scene coordinate system. This invariance does not eliminate localization error: the current, goal, and history images must still be localized consistently in the shared frame. The planar translation of ^t→g T_t→ g is converted to the model coordinate convention and divided by the waypoint spacing ℓ before forming t p_t. The consecutive history transformations provide the history-dependent entries of t m_t. Localization modularity. The retrieved reference images, NetVLAD descriptors, local keypoint descriptors, candidate global encodings, predicted scene coordinates, PnP hypotheses, and RANSAC inlier sets are internal quantities of the localization interface. They are not provided directly to the world-action model. The world-action model consumes only the current-to-goal relative transformation and the recent causal-motion profile. Consequently, the localization system can be replaced without changing the world-action-model architecture, provided that the replacement returns poses in a consistent metric frame. Possible alternatives include a traditional place-recognition and pose-estimation pipeline, visual SLAM, an external tracking system, or another learned relative-pose estimator. Known-scene scope. R-SCoRe requires a scene-specific reference database and a scene-coordinate prediction model trained from reference observations. Our Habitat experiment therefore follows a known-scene protocol. The fixed evaluation episodes are disjoint from the trajectories used to construct the localization database and fine-tune the navigation model, although the reference and evaluation trajectories belong to the same scene. This setup evaluates navigation to previously observed places from held-out trajectories rather than navigation in a completely unseen environment. Applying the same world-action model in an unseen scene would require an alternative shared-frame localization source, such as online mapping, visual SLAM, or a map-free relative-pose estimator. Once the relative-pose and motion conditions are available, the world-action-model architecture itself does not need to be changed. Online localization sequence. The goal image is localized once at the beginning of an episode and its estimated pose is cached. Every newly observed RGB frame is localized online. Only the current and previously observed images are used; neither future images nor future actions are available to the localization interface. For causal-motion estimation, at most four available history poses are retained. The pose history is updated only after the corresponding frame has been observed. The estimated-pose evaluation does not use ground-truth egomotion, and invalid localization estimates do not silently fall back to ground-truth poses. Causal estimated motion. Let i r_i and ψi _i denote the calibrated robot-frame position and yaw of history frame i. The recent translation scale is computed as the median nonzero displacement in waypoint units: d¯t=mediani∈t‖i+1−i‖2ℓ, d_t=median_i _t \| r_i+1- r_i \|_2 , (37) where tV_t contains the consecutive history pairs with nonzero translation. The recent rotation scale is the mean absolute wrapped yaw change: θ¯t=meani|atan2(sin(ψi+1−ψi),cos(ψi+1−ψi))|. θ_t=mean_i |atan2 ( ( _i+1- _i), ( _i+1- _i) ) |. (38) Before two valid history frames are available, d¯t d_t and θ¯t θ_t fall back to their dataset-level translation and yaw scales. If all available history translations are zero, d¯t d_t also falls back to the dataset-level translation scale. Its returned value is lower-bounded by 0.10.1. The remaining motion-profile entries are the dataset-level translation scale dsd_s, dataset-level yaw scale θs _s, and waypoint spacing ℓ . Habitat coordinate conversion. For Habitat, the R-SCoRe pose engine returns a camera-to-world transformation WC T_WC. The current-to-goal camera transformation is CtCg=WCt−1WCg. T_C_tC_g= T_WC_t^-1 T_WC_g. (39) Let =(tx,ty,tz) t=(t_x,t_y,t_z) denote its translation after applying the metric conversion factor. Under the Habitat camera convention, the goal-relative forward and left coordinates are Δxtg=tz,Δytg=−tx. x_t^g=t_z, y_t^g=-t_x. (40) To recover relative yaw, the goal camera’s forward axis (0,0,1)(0,0,1) T is transformed into the current camera frame: g=CtCg[001],Δθtg=atan2(−fg,x,fg,z). f_g= R_C_tC_g bmatrix0\\ 0\\ 1 bmatrix, _t^g=atan2(-f_g,x,f_g,z). (41) The translation is then divided by the waypoint spacing before forming the relative-pose condition. Habitat R-SCoRe settings. The input RGB observation is processed at an encoder size whose shorter side is 480480 pixels. The Habitat camera intrinsics correspond to a 90∘90 horizontal field of view; the focal length used by the pose solver is therefore set to half the image width, with the principal point at the image center. The original R-SCoRe evaluation considers 1010 retrieved candidates, whereas our Habitat implementation retrieves 2020. Retrieval is implemented with product-quantized nearest-neighbor search over the reference-image NetVLAD descriptors. For every retrieved candidate, its stored global scene encoding is concatenated with the local query descriptors before scene-coordinate prediction. We use a maximum PnP–RANSAC reprojection error of 1010 pixels and at most 10,00010,000 RANSAC iterations. A separate pose is estimated for every retrieved candidate, and the candidate producing the largest inlier set is selected. The R-SCoRe scene coordinates used by the Habitat localization map are converted to metres using a factor of 100100. The waypoint spacing is ℓ=0.2172m. =0.2172\,m. (42) The fixed dataset-level translation and yaw scales in the Habitat motion profile are ds=0.95824505,θs=0.87605652.d_s=0.95824505, _s=0.87605652. (43) Localization confidence. The RANSAC inlier count is converted into a bounded diagnostic confidence: cj=clip(|ℐj(r∗)|−1001000−100,0,1).c_j=clip ( |I_j^(r^*) |-1001000-100,0,1 ). (44) Thus, estimates with at most 100100 inliers receive zero confidence, while estimates with at least 10001000 inliers receive full confidence. The confidence and inlier count are recorded for localization diagnostics. They are not additional obstacle-avoidance, safety, or navigation-control signals. The relative-pose conditioner described in the main paper receives the four-dimensional (Δx,Δy,sinΔθ,cosΔθ)( x, y, θ, θ) condition. The numerical localization settings above describe the Habitat interface and do not necessarily apply to the trajectory-prediction datasets or the Go Stanford experiment. Appendix B Evaluation Protocol and Metric Definitions Trajectory prediction. All methods are evaluated on the same fixed 100 test queries per dataset with an eight-step prediction horizon. Let ^n,k∈ℝ2 p_n,k ^2 and n,k∗∈ℝ2 p^*_n,k ^2 denote the predicted and reference planar waypoint positions for query n at rollout step k, after converting all methods to a common waypoint coordinate system. Following the implementation used to produce the reported results, we compute a trajectory-level root-mean-square absolute trajectory error and a one-step relative pose error: ATE =1N∑n=1N1K∑k=1K‖^n,k−n,k∗‖22, = 1N _n=1^N 1K _k=1^K \| p_n,k- p^*_n,k \|_2^2, (45) RPE =1N∑n=1N1K−1∑k=1K−1‖(^n,k+1−^n,k)−(n,k+1∗−n,k∗)‖22, = 1N _n=1^N 1K-1 _k=1^K-1 \| ( p_n,k+1- p_n,k )- ( p^*_n,k+1- p^*_n,k ) \|_2^2, where K=8K=8. ATE measures the absolute deviation of the complete predicted trajectory, while RPE measures the error in consecutive relative translations. Neither metric includes rotational or image-reprojection error. The four-dataset average is the unweighted mean over RECON, SACSoN, TartanDrive, and SCAND. Closed-loop navigation. The Gibson evaluation uses 100 fixed validation episodes from the known Mosquito scene, a 22 m geodesic success threshold, and at most 100 executed actions. At each planning cycle, G2WAM observes an RGB frame, updates its causal history, estimates goal-relative pose and motion, predicts eight latent/action steps, executes only the first waypoint through VelocityXZYawMove, and replans after the next observation. The evaluated controller does not decode future RGB frames or add CEM, APF, depth-based safety control, persistent bypass, or anti-spin logic. After each executed action, the evaluator uses geodesic distance to trigger an oracle STOP when the agent is within 2 m. No success check is performed at reset, so every episode executes at least one action. Geodesic distance is otherwise not provided as a control input. Success rate (SR) is the fraction of successful episodes. Success weighted by path length (SPL) weights each success by the shortest-path length divided by the larger of that length and the executed path length. Distance to goal (DTG) is the mean final geodesic distance over all episodes, including failures. The model-only latency reported in the main text excludes localization, simulation, and action execution. The G2WAM-GT comparison uses oracle pose and causal motion; the deployed G2WAM setting uses image-estimated inputs. Appendix C Supplementary Code and Navigation Videos Code package. The anonymous supplementary archive provides the G2WAM model definition, evaluation entry points for eight-step trajectory prediction and Gibson navigation, pose and causal-motion interfaces, fixed test-split metadata, configuration files, and validation scripts. It records checksums for included files and identifiers for the frozen assets used in our experiments. Raw datasets and third-party components, including DINOv3, R-SCoRe, and Habitat-Sim, are not redistributed. The training implementation and pretrained checkpoints are withheld during anonymous review and will be released after acceptance. Accordingly, the archive documents the evaluation pipeline but is not a self-contained, weight-inclusive reproduction. Qualitative navigation videos. The ten paired videos show actual first-person RGB observations rendered by Habitat-Sim after executed actions, rather than images generated by either world model. Each pair uses the same Gibson Mosquito episode, starting observation, and goal image. For G2WAM, we replay the original evaluation actions and verify the geodesic distance-to-goal trace at every step. NWM is freshly rerun using its six-step distilled checkpoint because repeated closed-loop inference with the original checkpoint is impractically slow. NWM is stochastic, so an individual recording need not match the outcome of an earlier aggregate evaluation. Playback is aligned by executed action index rather than wall-clock inference time; after one side terminates, its final frame remains visible. Table 6: Outcome-selected paired Habitat recordings. S/F denotes success or failure under the 2 m threshold. Steps are executed actions, not video frames. These examples do not estimate full-test-set SR or SPL. Episode index Episode ID G2WAM Steps NWM Steps 92 3353 S 9 S 75 17 3403 S 21 F 100 29 3532 S 60 S 36 19 3537 S 32 F 100 59 3310 S 12 S 1 16 3527 S 25 S 4 64 3408 S 20 F 100 24 3557 S 46 F 100 1 3595 S 26 F 100 83 3485 F 100 F 100 The recordings were deliberately selected for qualitative inspection: four pairs succeed for both methods, five succeed only for G2WAM, and one fails for both. This outcome-conditioned subset is not representative of the complete 100-episode evaluation. Quantitative comparisons should therefore use the main evaluation table rather than these selected videos. Appendix D AI Use Statement Generative AI tools were used for language editing, literature search, drafting portions of the manuscript, software implementation, and assisting with the reproduction of baseline methods. All AI-assisted text, code, references, and baseline implementations were reviewed and verified by the authors. The authors take full responsibility for the final manuscript, methods, results, claims, and artifacts.