HUG-VAS: A Hierarchical NURBS-Based Generative Model for Aortic Geometry Synthesis and Controllable Editing.

Accurate, patient-specific vascular geometry is pivotal for diagnosis, planning, and device design, yet existing statistical shape modeling (SSM) pipelines rely on linear priors and topology-specific preprocessing that limit realism, scalability, and interoperability. We present HUG-VAS, a Hierarchical NURBS Generative framework for Vascular models, that unifies NURBS-based 3D shape encoding with diffusion-based generative modeling to synthesize fine-grained, CFD-ready aortic anatomies. HUG-VAS factorizes shape into (i) vessel centerlines generated by a denoising diffusion model and (ii) cross-sectional radius profiles synthesized by a classifier-free guided diffusion model conditioned on the centerline, thereby decoupling and preserving stochastic variability across these two anatomical layers. Beyond unconditional synthesis, we enable training-free, zero-shot conditional generation via diffusion posterior sampling from image-derived prompts (e.g., sparse 3D points, slice contours, or partial surface patches), supporting interactive semi-automatic segmentation, editing and robust reconstruction under degraded imaging. Trained on 21 patient-specific MRA cases, HUG-VAS generates multi-branch aortas with supra-aortic vessels whose biomarker distributions closely match the source cohort, and whose watertight NURBS outputs directly integrate with downstream CFD solvers. To our knowledge, HUG-VAS is the first SSM frameworks to unify NURBS parameterization, hierarchical diffusion, and DPS-based zero-shot conditional generation, enabling reconstruction and completion of vascular geometry from sparse, partial geometric priors without retraining.