Therapeutic antibodies are at the forefront of biotherapeutics, valued for their high target specificity and binding affinity. Despite their potential, optimizing antibodies for superior efficacy presents significant challenges in both monetary and time costs. Recent strides in computational and artificial intelligence (AI), especially generative diffusion models, have begun to address these challenges, offering novel approaches for antibody design. This review delves into specific diffusion-based generative methodologies tailored for antibody design tasks, de novo antibody design, and optimization of complementarity-determining region (CDR) loops, along with their evaluation metrics. We aim to provide an exhaustive overview of this burgeoning field, making it an essential resource for leveraging diffusion-based generative models in antibody design endeavors.