Bayesian optimisation (BO) is a powerful framework for sample-efficient optimisation of expensive black-box functions, but its application to high-dimensional discrete scientific design remains challenging. Local trust-region BO methods such as TuRBO address high dimensionality by restricting search to adaptively sized neighbourhoods. However, a direct discrete analogue based on edit distance can be poorly suited to structured discrete objects: neighbourhoods grow combinatorially, and metric proximity does not capture the dependencies that determine whether a design is plausible or useful. Motivated by the growing availability of pretrained generative models, we introduce GenTuRBO, which replaces the geometric trust region with an adaptively scaled proposal distribution defined by a pretrained generator. The generator provides a learned prior over discrete transformations, encoding coordinated changes without explicitly enumerating edit-distance neighbourhoods. GenTuRBO performs strongly across all three domains and achieves the highest mean final scores on Ehrlich sequence optimisation and Sokoban coordination.

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