We introduce IgDiff, an antibody variable domain diffusion model based on a general protein backbone diffusion framework which was extended to handle multiple chains. Assessing the designability and novelty of the structures generated with our model, we find that IgDiff produces highly designable antibodies that can contain novel binding regions. The backbone dihedral angles of sampled structures show good agreement with a reference antibody distribution. We verify these designed antibodies experimentally and find that all express with high yield. Finally, we compare our model with a state-of-the-art generative backbone diffusion model on a range of antibody design tasks, such as the design of the complementarity determining regions or the pairing of a light chain to an existing heavy chain, and show improved properties and designability.