Metal-organic frameworks (MOFs) are of immense interest in applications such as gas storage and carbon capture due to their exceptional porosity and tunable chemistry. Their modular nature has enabled the use of template-based methods to generate hypothetical MOFs by combining molecular building blocks in accordance with known network topologies. However, the ability of these methods to identify top-performing MOFs is often hindered by the limited diversity of the resulting chemical space. In this work, we propose MOFDiff: a coarse-grained (CG) diffusion model that generates CG MOF structures through a denoising diffusion process over the coordinates and identities of the building blocks. The all-atom MOF structure is then determined through a novel assembly algorithm. As the diffusion model generates 3D MOF structures by predicting scores in E(3), we employ equivariant graph neural networks that respect the permutational and roto-translational symmetries. We comprehensively evaluate our model's capability to generate valid and novel MOF structures and its effectiveness in designing outstanding MOF materials for carbon capture applications with molecular simulations.