Conclusion. We developed NGT to overcome a critical limitation of unconstrained generative AI in medicinal chemistry applications: generative AI 'hallucinates' compounds that cannot be made. NGT prioritizes compounds with desirable properties that can be readily made in the lab, accelerating the path from discovery to a potential drug. NGT's strength over other methods that search CSLs lies in 1) its scalability, encoding ever-growing CSLs logarithmically in space and lookup time , and 2) balancing exploration and exploitation to obtain a diverse set of scaffolds that satisfy desirable properties by learning a mass-covering policy enabled by a new family of α-divergences. Unlike synthon-growing based approaches , NGT is sensitive to non-additive properties (Table ). NGT outperformed synthon-growing based approaches in finding diverse compounds with low prevalence in the library satisfying narrow or non-linear properties (like Lee and QED) where other methods struggle. Diversity sampling boosted performance compared to random baselines and even HE, which often favors similar compounds. This makes NGT valuable for virtual screening where diverse chemical space exploration is crucial. With these advancements, NGT found a novel potent and selective hit for MC2R from a three trillion compound CSL despite the lack of training data for this challenging target. Our hit rate compared very favorably to that from a recent experimental HTS compound screen, although the top potency was slightly lower.