Spatial World Model: Spatially Structured Latent Dynamics and Planning

Latent world models have emerged as a compelling approach to learning environment dynamics through reward-free representation learning. However, their latent dynamics often remain entangled and geometrically unstructured, limiting their interpretability and utility for downstream planning. In this paper, we introduce Spatial World Model (SWM), a framework for learning spatially structured latent dynamics. SWM structures the latent space through two complementary geometric properties: orthogonality and directional ordering. Orthogonality enforces mutually orthogonal latent directions, while directional ordering arranges each latent-transition projection according to its corresponding state-transition component. These properties yield a spatially structured latent space that reflects the spatial organization of the environment. Building on this structure, we construct a goal-directed latent heuristic by projecting the current-to-goal latent displacement onto the learned directions. We incorporate this heuristic into Spatial-Aware Latent Planning (SLP), which guides search over a latent roadmap and composes local world-model predictions into long-horizon plans. Experiments on OGBench PointMaze validate the spatial structure learned by SWM and show that SLP outperforms comparison methods at larger goal offsets and longer execution horizons.