  We introduce a radiance representation that is both structured and fully
explicit and thus greatly facilitates 3D generative modeling. Existing radiance
representations either require an implicit feature decoder, which significantly
degrades the modeling power of the representation, or are spatially
unstructured, making them difficult to integrate with mainstream 3D diffusion
methods. We derive GaussianCube by first using a novel
densification-constrained Gaussian fitting algorithm, which yields
high-accuracy fitting using a fixed number of free Gaussians, and then
rearranging these Gaussians into a predefined voxel grid via Optimal Transport.
Since GaussianCube is a structured grid representation, it allows us to use
standard 3D U-Net as our backbone in diffusion modeling without elaborate
designs. More importantly, the high-accuracy fitting of the Gaussians allows us
to achieve a high-quality representation with orders of magnitude fewer
parameters than previous structured representations for comparable quality,
ranging from one to two orders of magnitude. The compactness of GaussianCube
greatly eases the difficulty of 3D generative modeling. Extensive experiments
conducted on unconditional and class-conditioned object generation, digital
avatar creation, and text-to-3D synthesis all show that our model achieves
state-of-the-art generation results both qualitatively and quantitatively,
underscoring the potential of GaussianCube as a highly accurate and versatile
radiance representation for 3D generative modeling. Project page:
https://gaussiancube.github.io/.
