From Latent Loops to Better Navigation: Understanding Diffusion-Based World Models with Cognitive-Map-Inspired Dynamics

Diffusion-based world models have recently demonstrated strong visual navigation performance without explicitly constructing maps, yet the latent mechanisms behind this capability remain unclear. We analyze diffusion-based navigation world models through the lens of cognitive map theory. Using persistent homology, we find that these models develop low-dimensional latent spatial structures during navigation generation, suggesting the emergence of cognitive-map-like representations. However, these structures are unstable across layers and long-horizon autoregressive rollouts, which may contribute to accumulated prediction drift. Motivated by this observation, we propose a brain-inspired framework that augments a frozen diffusion world model with a compositional cognition module. This module introduces structured, action-conditioned grid–place dynamics as an explicit spatial prior to stabilize latent spatial representations and improve long-horizon consistency. Experiments on real-world navigation datasets show improved prediction, navigation, and representation stability over strong diffusion-based baselines. Component ablations support the contribution of structured grid–place conditioning, while correlation analysis reveals an association between topological persistence and trajectory accuracy.