World-action models (WAMs) are emerging as a promising foundation for embodied control: rather than predicting actions alone, they learn representations that couple action generation with future world prediction. This coupling is often viewed as a source of robustness, interpretability, and safety, as a robot's action can in principle be checked against its imagined future. In this paper, we show that this assumption is fragile. We introduce BadWAM, a unified framework for modeling and evaluating World-Action Drift Attacks: a new class of WAM-specific adversarial attacks that use small visual perturbations to break the alignment between what a WAM imagines and what it executes. BadWAM characterizes this attack surface along two natural criteria: attack strength and stealthiness. When the adversary prioritizes disruption, BadWAM instantiates an action-only adversarial attack, which directly drives the model toward task-failing actions. When the adversary additionally prioritizes stealth, BadWAM instantiates an imagination-preserving adversarial attack, which seeks to induce harmful action shifts while keeping the model's predicted future close to its clean imagination. Together, these two attacks capture a spectrum of WAM-specific failures: from overt action hijacking to stealthier cases where the model appears to imagine a plausible future but executes a desynchronized action. We evaluate BadWAM across different variants of WAMs. Results show that our attacks substantially reduce task success rates under closed-loop execution. For example, our action-only attack reduces the model performance from 96.5\% to 43.1\% success. The results of our imagination-preserving attack further exposes a WAM-specific vulnerability: moderate future-preserving regularization can maintain strong attack performance while reducing future imagination drift.

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