Despite a surge of deep learning papers focused on generative models for small molecules, it remains difficult to out-compete more traditional, rule-based approaches such as a genetic algorithm (GA). In prior research, we introduced quality-diversity methods to de novo design of small molecules and showed that these methods -which explicitly balance exploitation and exploration -resolve stagnation issues and are more efficient in exploring chemical space than both deep learning models and genetic algorithms. In this work, we extend this approach by leveraging and integrating Bayesian optimisation methods to present a novel generative molecular model, which we call Bayesian Illumination. This algorithm produces a larger diversity of high-performing molecules and further improves search efficiency compared to genetic algorithms, deep learning approaches and standard qualitydiversity methods.