Generative AI has the potential to revolutionize drug discovery. Yet, despite recent advances in deep learning, existing models cannot generate molecules that satisfy desired physicochemical properties. Herein, we describe a novel generative chemistry AI combining diffusion with multi-objective optimization for structure-based drug design. Differentiable scoring functions guide the latent variables of the diffusion model to explore uncharted chemical space and generate novel ligands in silico, optimizing a plurality of target physicochemical properties. We demonstrate our platform's effectiveness by generating ligands with optimized binding affinity and synthetic accessibility on two benchmark sets. Our workflow produces ligands with binding affinities over 10%-20% higher than the next best state-of-the-art on each set, producing molecules with better synthetic accessibility than all but one other deep learning method. Additionally, we compare our platform against a traditional virtual screen of a large database of drug-like molecules. We show that we can generate molecules for a range of important disease-related targets with better binding affinity and synthetic accessibility than any molecule found in the virtual screen while being over 100× faster and less expensive to run. Our pipeline is the first to produce molecules with better binding affinities than the experimentally observed ligands on a test set of experimental complexes. Our platform can also accommodate other scoring functions (e.g. ADME-Tox) to accelerate hit-finding, hit-to-lead, and lead optimization for drug discovery.