In this work, we present IgFlow, an SE(3)-flow matching model for de novo design of antibody structures. We focus on generating novel variable domain regions of the antibody and assess the performance of our model on 1) unconditional heavy and light chain generation and 2) framework-conditional loop design of the complementarity-determining regions (CDRs). Our results show that IgFlow generated antibodies are structurally similar to naturally observed antibodies. We compare our approach to IgDiff, an SE(3)-diffusion model for unconditional variable domain generation, on designability. Furthermore, we benchmark IgFlow and IgDiff on two conditional CDR inpainting tasks commonly encountered in antibody design. We find that IgDiff and IgFlow are both performant at unconditionally designing antibodies, and that IgFlow conditionally designs full CDR loops with higher self-consistency than IgDiff. Overall, our approach offers an alternative approach for antibody generation with additional computational benefits, including sample data efficiency and inference speed.