Achieving robust and generalizable manipulation across diverse environments remains a fundamental challenge in embodied robotics. Recent world action models achieve strong in-domain performance, yet their gains do not extend proportionally to out-of-distribution scenarios. We attribute this to a structural mismatch between visual and action modalities, whose intrinsically heterogeneous manifolds cause joint optimization to disproportionately degrade action robustness under distribution shift. To address this, we propose MV-WAM, a novel end-to-end framework that jointly models visual prediction, action generation, and value estimation designed to effectively leverage video priors during both training and inference for enhanced action generalization. Key to this unification is a cross-modality causal mask that hierarchically grounds actions in predicted video frames and value function tokens in both modalities. To further narrow the generalization gap, MV-WAM adopts a manifold-aware optimization scheme that explicitly accounts for the structural heterogeneity across modalities. Finally, MV-WAM introduces a progress-value regulation mechanism that estimates task completion and detects misalignment between predicted frames and generated actions, enabling the policy to autonomously identify execution deviations and recover through value-guided rollback. On the RoboTwin simulation, MV-WAM achieves a 55.7% mean success rate on random scenarios without any randomized action supervision, outperforming the strongest baseline by 29.3%. MV-WAM achieves a 77.5% mean success rate across four real-world tasks of varying difficulty on a dual-arm robot. Our results demonstrate that manifold-aware cross-modal alignment is essential for robust policy generalization, offering a path toward deployable robotic manipulation.

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