GeoTrans: Geometry-Aware State Transport for Training-Free World Model Acceleration

Diffusion-based world models generate controllable videos through iterative denoising, but repeated transformer evaluations over long spatiotemporal sequences make inference expensive. Training-free caching exploits temporal redundancy, yet temporal prediction alone does not capture the shared state evolution of geometrically corresponding tokens. Our analysis reveals that geometric correspondence organizes coherent state changes while substantial residual variation remains, motivating geometry-aware latent state transport. We propose GeoTrans, a training-free acceleration framework that determines when to refresh anchors, how to construct geometric transport, and what state update to accept. GeoTrans adaptively refreshes anchors using temporal drift and a horizon limit, decomposes proposed displacements into geometric shared and residual components, and estimates their gains online in closed form from completed anchor transitions. Geometry defines the transition structure, while anchor transitions determine the accepted update, requiring no additional transformer evaluations or gradient computation for gain estimation. Experiments on Voyager and Aether achieve $4.25\times$ and $1.96\times$ acceleration, respectively, with improved generation fidelity over WorldCache. Controlled ablations further isolate the benefit of geometric state transport.