Reconstructing three-dimensional (3D) coronary anatomy from sparse angiographic views could support percutaneous coronary intervention, but limited angular coverage and imperfect vessel segmentations introduce substantial geometric ambiguity. We propose a vessel-specific reconstruction framework combining a learned 3D diffusion prior, visual-hull initialization, and projection-based data consistency. The unconditional diffusion model is trained on coronary vessel masks without paired 2D--3D data and reused across different view counts without retraining. During inference, a scaled visual hull initializes reconstruction, while projection-based updates constrain diffusion refinement using patient-specific vessel observations. We evaluated the framework on simulated angiograms derived from ImageCAS computed tomography angiography volumes using two, four, and eight views at two contrast levels. Across 50 evaluation coronary-tree cases, the proposed method achieved higher mean Dice and clDice than visual hull, deep image prior (DIP), and hash-grid implicit neural representation (INR) at all view counts under reduced contrast. With eight views, improvements over DIP, the best-performing baseline at lower contrast, were approximately 0.13 in Dice and 0.22 in clDice. At higher contrast, performance remained competitive with hash-grid INR, the best-performing eight-view baseline. The preferred diffusion starting timestep depended on observation quality and view count, with excessive refinement reducing accuracy at higher contrast. Projection guidance improved both metrics across all conditions. Averaging stochastic reconstructions further improved accuracy, while sample disagreement localized errors with average-precision gains of 0.14--0.21 over error prevalence. These findings support diffusion-prior reconstruction from sparse vessel observations, although clinical validation remains necessary.

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