Occupancy prediction provides critical geometric and semantic understanding for robotics but faces efficiency-accuracy trade-offs. Current dense methods suffer computational waste on empty voxels, while sparse query-based approaches lack robustness in diverse and complex indoor scenes. In this paper, we propose DiScene, a novel sparse query-based framework that leverages multi-level distillation to achieve efficient and robust occupancy prediction. In particular, our method incorporates two key innovations: (1) a Multi-level Consistent Knowledge Distillation strategy, which transfers hierarchical representations from large teacher models to lightweight students through coordinated alignment across four levels, including encoder-level feature alignment, query-level feature matching, prior-level spatial guidance, and anchor-level high-confidence knowledge transfer and (2) a Teacher-Guided Initialization policy, employing optimized parameter warm-up to accelerate model convergence. Validated on the Occ-Scannet benchmark, DiScene achieves 23.2 FPS without depth priors while outperforming our baseline method, OPUS, by 36.1% and even better than the depth-enhanced version, OPUS†. With depth integration, DiScene† attains new SOTA performance, surpassing EmbodiedOcc by 3.7% with 1.62$\times$ faster inference speed. Furthermore, experiments on the Occ3D-nuScenes benchmark and in-the-wild scenarios demonstrate the versatility of our approach in various environments. Code and models can be accessed at https://github.com/getterupper/DiScene.