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, this is the first SSM framework that bridges image-derived priors and generative shape synthesis through a unified combination of NURBS parameterization, hierarchical diffusion, and DPS, enabling a practical path from limited clinical anatomic information to simulation-ready vascular geometry.