Visual world models enable robotic planning by predicting future observations, but dense latent-state propagation and sample-intensive trajectory optimization incur high inference latency and peak memory usage, limiting real-time deployment on resource-constrained platforms. Existing sparse world-model acceleration methods either rely on unguided token sparsification, which may discard planning-relevant information and restrict achievable sparsity, or introduce heavy auxiliary modules and cumbersome multi-stage training pipelines. In this work, we present Scope-WM, an efficient visual world model that scopes computation to prediction-relevant latent regions and promising action sequences. Scope-WM distills prediction relevance into a lightweight action-conditioned selector and applies full dynamics prediction only to a compact subset of selected tokens. It updates the remaining tokens using a compact summary of foreground states and their changes, allowing the background to perceive foreground dynamics without costly token-to-token interactions. During planning, Scope-WM preserves and reuses high-quality action sequences discovered during the initial MPC search, focusing subsequent search under reduced rollout budgets. The resulting pipeline requires only a one-off selector distillation followed by a single joint training stage for the sparse world model. On the challenging Push-T task, Scope-WM reduces peak GPU memory usage and planning time to $18.1\%$ and $14.3\%$ of those of dense DINO-WM, respectively, corresponding to a $6.97\times$ planning speedup, while maintaining competitive task performance. Further evaluations across five diverse visual planning tasks demonstrate the general applicability of Scope-WM. Code is available at https://github.com/ChunZheng2022/Scope-WM.

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