3D Gaussian Splatting (GS) have achieved considerable improvement over Neural Radiance Fields in terms of 3D fitting fidelity and rendering speed. However, this unstructured representation with scattered Gaussians poses a significant challenge for generative modeling. To address the problem, we introduce GaussianCube, a structured GS representation that is both powerful and efficient for generative modeling. We achieve this by first proposing a modified densification-constrained GS fitting algorithm which can yield high-quality fitting results using a fixed number of free Gaussians, and then re-arranging the Gaussians into a predefined voxel grid via Optimal Transport. The structured grid representation allows us to use standard 3D U-Net as our backbone in diffusion generative modeling without elaborate designs. Extensive experiments conducted on ShapeNet and OmniObject3D show that our model achieves state-of-the-art generation results both qualitatively and quantitatively, underscoring the potential of GaussianCube as a powerful and versatile 3D representation.

翻译：三维高斯溅射（Gaussian Splatting, GS）在三维拟合精度和渲染速度方面相较于神经辐射场取得了显著提升。然而，这种由离散高斯体构成的无结构表示给生成建模带来了重大挑战。为解决该问题，我们提出了一种兼具强大性能与高效性的结构化GS表示方法——GaussianCube。具体而言，我们首先提出一种改进的稠密化约束GS拟合算法，能够在固定自由高斯体数量的情况下实现高质量拟合，随后通过最优传输（Optimal Transport）将高斯体重新排列至预定义的体素网格中。这种结构化网格表示使我们能够直接使用标准三维U-Net作为扩散生成建模的主干网络，无需繁琐的设计。在ShapeNet和OmniObject3D数据集上的大量实验表明，我们的模型在定性与定量指标上均达到最先进的生成结果，彰显了GaussianCube作为高效且通用的三维表示方法的潜力。