GaussianCube: Structuring Gaussian Splatting using Optimal Transport for
  3D Generative Modeling
Authors: name: Bowen Zhang, name: Yiji Cheng, name: Jiaolong Yang, name: Chunyu Wang, name: Feng Zhao, name: Yansong Tang, name: Dong Chen, name: Baining Guo

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.