提出统一多模态控制的手术世界模型，生成更真实、连贯的手术视频。

Controllable surgical world models can provide a generative foundation for surgical artificial intelligence and simulation by synthesizing realistic instrument--tissue interactions. However, existing methods lack a unified multimodal control paradigm, while direct fusion of heterogeneous visual conditions often causes anatomical distortion, instrument appearance drift, and temporally inconsistent interactions. In this work, we propose {Surg-UniWorld}, a unified surgical world model with multimodal control experts. Surg-UniWorld first constructs a {Hierarchical Surgical Anchor} from first-frame appearance and hierarchical semantic masks to preserve persistent scene identity, anatomical organization, and interaction boundaries. {Anchor-Relative Modality Experts} then interpret edge, depth, and optical-flow evidence relative to the shared anchor, capturing complementary boundary, geometric, and motion information. A {Multimodal Control Expert} further performs contribution-preserving stage-wise composition of the activated modality increments and generates control hints for the Wan2.2 video diffusion backbone. To support multimodal surgical world modeling, we further construct Cholec80-SurgWAM, a benchmark for controllable surgical video generation. Extensive experiments demonstrate that Surg-UniWorld consistently outperforms existing controllable video generation methods and surgical world-model baselines in generation quality, temporal consistency, and multimodal controllability.