Vascular diseases pose a significant threat to human health, with X-ray angiography established as the gold standard for diagnosis, allowing for detailed observation of blood vessels. However, angiographic X-rays expose personnel and patients to higher radiation levels than non-angiographic X-rays, which are unwanted. Thus, modality translation from non-angiographic to angiographic X-rays is desirable. Data-driven deep approaches are hindered by the lack of paired large-scale X-ray angiography datasets. While making high-quality vascular angiography synthesis crucial, it remains challenging. We find that current medical image synthesis primarily operates at pixel level and struggles to adapt to the complex geometric structure of blood vessels, resulting in unsatisfactory quality of blood vessel image synthesis, such as disconnections or unnatural curvatures. To overcome this issue, we propose a self-supervised method via diffusion models to transform non-angiographic X-rays into angiographic X-rays, mitigating data shortages for data-driven approaches. Our model comprises a diffusion model that learns the distribution of vascular data from diffusion latent, a generator for vessel synthesis, and a mask-based adversarial module. To enhance geometric accuracy, we propose a parametric vascular model to fit the shape and distribution of blood vessels. The proposed method contributes a pipeline and a synthetic dataset for X-ray angiography. We conducted extensive comparative and ablation experiments to evaluate the Angio-Diff. The results demonstrate that our method achieves state-of-the-art performance in synthetic angiography image quality and more accurately synthesizes the geometric structure of blood vessels. The code is available at https://github.com/zfw-cv/AngioDiff.