Identifying new compounds or materials with a desired set of properties is a complex challenge. The computational task primarily involves two stages: the generation of physically sound candidate structures, and their subsequent characterization using computational methods. For the primary characterization step of assessing structural stability, density functional theory (DFT) offers a reasonable trade-off between accuracy and computation cost. Recently, advances in accurate machine-learned force fields (MLFFs) have substantially accelerated the stability evaluation at only a small cost in accuracy. However, the vast search space, i.e. all the plausible conformations of molecules or crystals at a given stoichiometry, renders an exhaustive exploration unfeasible for all but the most trivial cases. Hence, the generation and selection of candidate structures is an equally important challenge to address. Historically, several approaches, including substitution into known structures based on data mined rules, simulated annealing, and various methods based on evolutionary algorithms, have been employed to address this challenge. While these methods are able to cover a wide range of structures, they are often limited by their underlying assumptions and require a frequent evaluation of the potential energy (PE). Furthermore, the vast knowledge about stable structures is at best only included as heuristic rules to filter the number of candidates to be considered.