Cross-modality medical image synthesis is a critical topic and has the potential to facilitate numerous applications in the medical imaging field. Despite recent successes in deep-learning-based generative models, most current medical image synthesis methods rely on generative adversarial networks and suffer from notorious mode collapse and unstable training. Moreover, the 2D backbone-driven approaches would easily result in volumetric inconsistency, while 3D backbones are challenging and impractical due to the tremendous memory cost and training difficulty. In this paper, we introduce a new paradigm for volumetric medical data synthesis by leveraging 2D backbones and present a diffusion-based framework, Make-A-Volume, for cross-modality 3D medical image synthesis. To learn the cross-modality slice-wise mapping, we employ a latent diffusion model and learn a low-dimensional latent space, resulting in high computational efficiency. To enable the 3D image synthesis and mitigate volumetric inconsistency, we further insert a series of volumetric layers in the 2D slice-mapping model and fine-tune them with paired 3D data. This paradigm extends the 2D image diffusion model to a volumetric version with a slightly increasing number of parameters and computation, offering a principled solution for generic cross-modality 3D medical image synthesis. We showcase the effectiveness of our Make-A-Volume framework on an in-house SWI-MRA brain MRI dataset and a public T1-T2 brain MRI dataset. Experimental results demonstrate that our framework achieves superior synthesis results with volumetric consistency.