ATLAS: Aligned Transport of Latent Structure for Reliable World Model Planning

Latent world models learn action-conditioned dynamics in representation space and often score candidate actions by Euclidean distance to a goal representation. Joint training typically regularizes the representation to prevent collapse, but the resulting representation geometry also determines how terminal errors are weighted during planning. We show that accurate prediction and noncollapsed representations do not guarantee a task-aligned latent planning cost: isotropic Gaussian regularization can induce a geometry that ranks feasible outcomes differently from the task cost. To address this mismatch, we introduce AnisoWM with $Λ$Reg, which replaces the fixed isotropic Gaussian target with a learnable diagonal covariance under fixed-trace and anisotropy constraints. The prediction objective, predictor architecture, and Euclidean planner remain unchanged; the target is used only during training. Our analysis characterizes the prediction-driven allocation of target variance, its dependence on the training distribution, and the conditions under which the induced metric reduces planning regret. Across four visual control environments, AnisoWM improves planning success over LeWorldModel in all four. Its latent planning cost also shows better agreement with task outcomes. Project website: https://rkdrn79.github.io/AnisoWM-page/

Latent world models can achieve accurate latent prediction yet still differ substantially in downstream planning performance. We argue that a key source of this discrepancy lies in the structure of action-induced latent transitions. We formalize action-identifiability through Bayes inverse risk, characterizing how much uncertainty about an action remains after observing the transition it induces. Model-predicted transitions can become highly self-decodable while encoding a domain-specific action relationship that fails to transfer to real environment transitions. We characterize this mismatch through cross-domain inverse transfer, instantiated as the Action-Consistency Transfer Matrix (ATM), a $2\times2$ inverse-risk matrix over real and predicted transition domains. Across TwoRoom, PushT, and OGBench-Cube, true-transition action-identifiability tracks downstream planning substantially better than standard prediction loss, while the full ATM reveals highly self-decodable yet cross-domain-inconsistent predicted transitions. Controlled interventions on the two domains further produce distinct transition structures and planning outcomes, supporting this decomposition. The same diagnostics also support lightweight model screening, reaching 98.81% pairwise ranking accuracy for candidates separated by more than 5% success.

Modern vision-based world models can represent observations as compact yet expressive latent manifolds, but fast goal-oriented planning in these spaces remains challenging. This raises a central question: when does a learned representation simplify control, rather than merely enabling prediction? We study this question in a pretrained LeWorldModel, whose latent geometry is regularized for smoothness and uniformity. Our key insight is that, under such geometry, planning can be amortized into a latent inverse-dynamics mapping instead of requiring online search. We therefore replace iterative planning with a lightweight Goal-Conditioned Inverse Dynamics Model (GC-IDM) that maps the current latent state, goal latent state, and remaining horizon directly to the next action. Empirically, across four benchmark environments spanning navigation, contact-rich manipulation, and continuous control, our controller matches or exceeds CEM in seven of eight environment-protocol settings while reducing per-decision cost by 100-130x. A broader sweep over test-time planners (CEM, MPPI, iCEM, and gradient-based methods) shows that this result is not specific to a particular optimizer. These findings suggest that much of the structure recovered by test-time planning is already locally encoded in the latent representation. More broadly, our results indicate that sufficiently structured latent spaces can shift part of the planning burden from online optimization to learned inference. Our code is publicly available at https://github.com/hdnndh/Latent-Geometry-Beyond-Search-Amortizing-Planning-in-World-Models .