World Action Models (WAMs) can improve robot learning by jointly predicting future visual states and actions, but generating a visual future at every replanning step is expensive and sometimes unnecessary. This raises a critical question: when should a robot policy imagine the future? In this paper, we propose Bind-WAM, a binding-uncertainty-guided WAM for selective future imagination. Bind-WAM introduces language-object binding uncertainty, selectively invoking joint future-action generation when the current observation does not support stable task-relevant action generation. An offline labeling pipeline uses complete demonstrations and action context to identify task-relevant objects and detect reference mismatch, invisibility, and identity drift. The resulting pseudo-labels supervise a lightweight router that predicts binding uncertainty from the current observation and language instruction. At inference, a shared WAM policy invokes selective future imagination according to the predicted uncertainty and its change between consecutive replanning steps. Simulation and real-world experiments demonstrate that Bind-WAM can establish binding uncertainty as a strong, interpretable signal for selective future imagination.

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