Angiography imaging is a medical imaging technique that enhances the visibility of blood vessels within the body by using contrast agents. Angiographic images can effectively assist in the diagnosis of vascular diseases. However, contrast agents may bring extra radiation exposure which is harmful to patients with health risks. To mitigate these concerns, in this paper, we aim to automatically generate angiography from non-angiographic inputs, by leveraging and enhancing the inherent physical properties of vascular structures. Previous methods relying on 2D slice-based angiography synthesis struggle with maintaining continuity in 3D vascular structures and exhibit limited effectiveness across different imaging modalities. We propose VasTSD, a 3D vascular tree-state space diffusion model to synthesize angiography from 3D non-angiographic volumes, with a novel state space serialization approach that dynamically constructs vascular tree topologies, integrating these with a diffusion-based generative model to ensure the generation of anatomically continuous vasculature in 3D volumes. A pre-trained vision embedder is employed to construct vascular state space representations, enabling consistent modeling of vascular structures across multiple modalities. Extensive experiments on various angiographic datasets demonstrate the superiority of VasTSD over prior works, achieving enhanced continuity of blood vessels in synthesized angiographic synthesis for multiple modalities and anatomical regions.