Trustworthy Imagination in Embodied World Models: Structural Constraints, Reality Anchoring, and Trust Adjudication

World models provide embodied agents with a mechanism for planning, policy improvement, and adaptation through imagined futures before physical‐world execution. However, such imagination is useful only when it is trustworthy: predicted futures must respect action dependence, temporal order, task intent, embodiment, contact, and the limits of available real‐world evidence. This survey organizes recent world‐model research around a mechanism‐level question: which design mechanisms make imagined futures reliable enough to guide control? We identify three coupled governance roles that intervene at different points in the evidence chain. Structural constraint shapes which futures may be imagined through causal rollout and autoregressive memory, predictive abstraction, conditioned and controllable generation, and physical structure, signals, and constraints. Reality anchoring ties imagined futures to real evidence through data‐scaled and cross‐embodied priors, perceptual and geometric anchors, and reality‐grounded post‐training loops. Trust adjudication determines how imagined futures may be used through rollout constraints and scoring, runtime diagnostics and response, and offline evaluation and benchmarks. Overall, this mechanism‐first taxonomy clarifies why visual plausibility is not enough: reliable imagination depends on coordinating what the model is allowed to generate, how its predictions are anchored to evidence, and when those predictions are permitted to influence downstream decisions.