Uranyl peroxide clusters, formed from uranyl ions, peroxide and other ligands, exhibit complex structural diversity and have significant potential in nuclear chemistry applications. Theoretical prediction is essential for atomic-level understanding of their formation and stability, offering insights where experiments face challenges from uranium's radioactivity and complex coordination. However, their large size and varied topologies pose challenges for theoretical study. In this work, we introduce Uni-Gen, a deep learning model based on the Uni-Mol framework, which generates uranyl cluster structures by leveraging topological similarities with carbon clusters, particularly fullerene. This newly-developed Uni-Gen not only validates the stability of the U₂₈ uranyl cluster consistent with previous experimental data, but also discovers a more stable U₄₄ uranyl cluster than the previously reported structure, and most notably, predicts the previously unreported isomers of the U₃₈ uranyl cluster. Our results demonstrate that Uni-Gen is a powerful tool for predicting diverse potentially stable uranyl cluster structures, thereby enriching our understanding of the stability landscape of uranyl clusters and offering potential for further exploration of novel uranyl materials and chemical phenomena.