World Action Models (WAMs) leverage pretrained video generative models for robotic control by jointly predicting future visual observations and actions. The visual prediction objective plays a key role in adapting pretrained video representations to the target robot domain. Yet standard visual prediction inherited from video pretraining treats all visual regions uniformly, despite their differing relevance to robotic control. We therefore investigate the spatial allocation of visual supervision in WAMs and show that focusing supervision on dynamic regions can substantially improve policy performance. Building on this finding, we introduce Motion-Guided Asymmetric Prediction (MoGAP), which augments WAM training with motion-focused visual prediction. MoGAP allocates noise asymmetrically across regions, training the model to reconstruct more heavily corrupted dynamic regions using less corrupted static regions as context. MoGAP is trained alongside standard video-action prediction through a training-only auxiliary prediction path within the shared video diffusion backbone. It uses motion cues derived directly from training videos, requiring neither an external teacher nor additional modalities. Across robot manipulation benchmarks and WAM architectures, MoGAP consistently improves policy performance, increasing success rates on the GR-1 tabletop benchmark from 38.8% to 47.5% for Fast-WAM (Wan2.2-5B) and from 52.3% to 62.3% for Cosmos3-Nano.

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