In therapeutic antibody design, achieving a balance between optimizing binding affinity subject to multiple constraints, and sequence diversity within a batch for experimental validation presents an important challenge. Contemporary methods often fall short in simultaneously optimizing these attributes, leading to inefficiencies in experimental exploration and validation. In this work, we tackle this problem using the latest developments in constrained latent space Bayesian optimization. Our methodology leverages a deep generative model to navigate the discrete space of potential antibody sequences, facilitating the selection of diverse, high-potential candidates for synthesis. We also propose a novel way of training VAEs that leads to a lower dimensional latent space and achieves excellent performance under the data-constrained setting. We validate our approach in vitro by synthesizing optimized antibodies, demonstrating consistently high binding affinities and preserved thermal stability.