Recently, it has been asserted 83 that to progress the research field, novel generative molecular models must demonstrate a clear advantage over genetic algorithms. Traditional deep generative models and genetic algorithms have struggled to consistently deliver optimised small molecules, either due to inefficiencies in information utilisation or evolutionary stagnation. In this paper, we introduce Bayesian Illumination, a novel approach that combines Gaussian processes with quality-diversity methods to address these shortcomings. Through an extensive series of molecular optimisation tasks, -ranging from drug rediscovery and multi-property optimisation to efficient power conversion and the design of protein binders -based on three independent benchmarking suites, we robustly show that Bayesian Illumination displays state-of-the-art efficiency in finding optimal molecular structures in chemical space. In addition, it is worth noting that Bayesian Illumination also generates a larger diversity of high-scoring molecules than a standard quality-diversity method without Bayesian optimisation.