World Action Models (WAMs) improve robot policy learning by jointly modeling future visual dynamics and actions. However, their scalability and generalization remain constrained by their reliance on costly expert demonstrations. We challenge this by asking whether future supervision for WAMs must originate from target-task expert trajectories. In this paper, we propose Vid2WAM, an offline distillation framework that transfers visual diffusion priors from a large video foundation model into a compact WAM student. Given an observation and language instruction, Vid2WAM distills supervision through two complementary channels: task-conditioned future rollouts directly supervise the student's future prediction branch, while an inverse dynamics model recovers embodiment-specific pseudo-actions for action learning. To robustly integrate synthetic and real supervision, we introduce source-aware residual action adaptation that learns source-specific corrections around a shared action backbone and mitigates interference from noisy pseudo-actions. During inference, both the video teacher and inverse dynamics model are discarded, leaving only the WAM student for efficient deployment. Simulation and real-world experiments demonstrate that Vid2WAM improves novel-task generalization and data efficiency under limited expert demonstrations while preserving low-latency inference.

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