CoGeo-WAM: Controllable Geometry Adaptation for World Action Models

World action models (WAMs) have demonstrated impressive robotic manipulation capabilities by jointly modeling future visual dynamics and actions. However, their visual representations are largely learned from RGB videos without explicit geometric perception, creating a mismatch with the inherently 3D nature of physical interaction. Existing approaches can strengthen spatial awareness through explicit geometry modeling, but often introduce additional geometric inputs. Moreover, geometry-oriented adaptation can alter useful pretrained representations, while its utility varies across manipulation contexts, making uniform geometry adaptation potentially suboptimal. To this end, we propose CoGeo-WAM, a framework for controllable geometry adaptation in world action models that combines implicit geometry alignment with adaptive geometry control. We align intermediate WAM video representations with 3D-aware features from a frozen pretrained 3D vision model and capture the resulting geometry-aligned adaptation in a LoRA residual branch, requiring no explicit geometric inputs or additional geometry model at inference time. A context-guiden controller then dynamically modulates this branch, allowing the model to selectively exploit geometric adaptation and preserve its pretrained video-action prior in different manipulation contents. Extensive experiments across multiple simulation benchmarks, real-world manipulation tasks, and different WAM backbones demonstrate that CoGeo-WAM consistently improves manipulation performance and outperforms both the original world action models and static geometry adaptation.