Image compression fundamentally seeks to maximize information preservation under limited bitrate constraints. Existing methods either treat images as collections of pixels for rate-distortion optimization, or leverage generative model priors to synthesize perceptually pleasing reconstructions, yet neither explicitly models the causal dependency structure underlying image regions, leaving rich intra-image causal information unexploited. This paper proposes a world-model-driven image compression framework that models natural images as structured slices of the physical world governed by causal constraints. We define causal anchors — the primitive world elements encoding the scene's causal dependency structure — and provide an information-theoretic justification for prioritizing bitrate allocation toward these anchors, proving that stronger world model predictive capacity yields greater compression gains from anchor-biased rate allocation. The encoder performs hierarchical causal decomposition via chain-of-thought reasoning to precisely localize causal anchors and construct a non-uniform rate allocation mask; the decoder takes causal anchors as the logical seed and leverages the world model's causal inference capability to perform chain-based scene reassembly for high-fidelity reconstruction. Experiments demonstrate that the proposed method substantially outperforms existing approaches across all metrics at ultra-low bitrates.