4D-WAM: Infusing Spatiotemporal Awareness into World Action Models through Trajectory Fields

Building on recent advances in world models, World Action Models (WAMs) jointly model video prediction and action generation. However, they typically represent videos in 2D pixel space, creating a representation gap with 3D space in which robotic actions are executed. Recent 3D approaches introduce 3D information, but fail to fully exploit the dynamics of 3D structures. In this work, we propose 4D-WAM, a model-agnostic training strategy that injects spatiotemporal knowledge from 3D trajectory fields into WAMs through representation alignment. To this end, we introduce two complementary objectives: 1) motion alignment, which aligns temporal feature variations across adjacent frames and encourages the model to build local 4D awareness during training, and 2) destination alignment, which guides the model to infer the final destination from the source frame by minimizing the gap between their attention-like similarity distributions. Together, these objectives provide both local motion supervision and long-horizon goal guidance, enabling WAMs to learn trajectory-level spatiotemporal representations. Extensive in-distribution and out-of-distribution experiments across different base models demonstrate the model's improvements in spatial understanding, execution precision, robustness, generalization, and versatility.