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To address this, we propose VesselSim, a two-stage framework for universal 3D blood vessel segmentation that eliminates the need for real annotated data during training. First, we introduce a stochastic, geometry-driven vascular simulation framework that models recursive branching, curvature-controlled growth, and collision-aware topology, followed by domain-randomized intensity synthesis to generate 16,500 anatomically plausible 3D angiographic volumes. Second, a 3D U-Net is trained solely on this synthetic data. 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