This paper describes a new approach for the reconstruction of complete 3-D arterial trees from partially incomplete image data. We utilize a physiologically motivated simulation framework to iteratively generate artificial, yet physiologically meaningful, vasculatures for the correction of vascular connectivity. The generative approach is guided by a simplified angiogenesis model, while at the same time topological and morphological evidence extracted from the image data is considered to form functionally adequate tree models. We evaluate the effectiveness of our method on four synthetic datasets using different metrics to assess topological and functional differences. Our experiments show that the proposed generative approach is superior to state-of-the-art approaches that only consider topology for vessel reconstruction and performs consistently well across different problem sizes and topologies.