Learning Differentiable Hierarchies in 3D Gaussian Splatting

Although 3D Gaussian Splatting (3DGS) has achieved impressive performance in real-time rendering, its unordered Gaussians make level-of-detail (LoD) construction and model compression highly challenging, limiting its applicability in customized scenarios. In this work, we propose a learning-based Gaussian hierarchy representation that ranks Gaussians by their contribution to the scene, enabling flexible LoD representations across arbitrary Gaussian counts. We first introduce a unified, continuous formulation and metric for Gaussian hierarchy. Then, we introduce a hierarchy-based modulated rendering method built upon a Differentiable Decreasing Step Function, which enables efficient hierarchy learning while maintaining approximately equivalent rendering. Moreover, we develop a PDF-Guided Active-Region Sampling strategy that encourages the learned hierarchy to become widely distributed within its value range. Our method requires no additional training stages and produces Gaussian hierarchies within training time comparable to classical 3DGS. Experiments on multiple datasets show that our approach achieves performance comparable to or surpassing state-of-the-art methods in both LoD rendering and model pruning.