Rethinking 3D Shape Generation: Diffusion over Superquadrics

Diffusion models have advanced 3D shape generation, yet most methods still denoise in high-cardinality spaces (e.g., voxel/SDF grids, meshes, or point clouds), which is computationally and memory intensive and makes it difficult to scale in terms of both higher resolution and stronger controllability. We rethink the diffusion representation and propose to move diffusion from dense geometry to compact geometric primitives, representing each shape as a small set of superquadrics. Instead of operating on thousands to millions of geometric representation values, we leverage 7KB superquadric parameters (pose, size, and shape), drastically reducing diffusion-state dimensionality and per-step compute/memory. Our diffusion-over-superquadrics improves scalability by supporting broader capabilities (e.g., resolution-free point-cloud decoding, part-level editing, and constraint-based design) and achieving competitive surface-fidelity and distributional performance on standard benchmarks after point-cloud decoding, while enabling efficient generation within 0.6s per shape for most conditions.

Many AI systems can now generate 3D objects, but they often do so by working with thousands or millions of small geometric elements, such as points, grids, or surface pieces. This makes 3D generation expensive and can also make it difficult for users to directly control the structure of the generated object. We propose a different way to generate 3D shapes. Instead of asking the model to build every tiny geometric detail directly, we represent an object as a small set of simple 3D building blocks, called superquadrics, which can describe rounded or box-like parts. Our method learns to generate these building blocks and their positions, sizes, and shapes. This compact representation makes generation faster and more memory-efficient, while still producing competitive 3D shapes. Because each building block has a clear meaning, the generated shapes can also be edited more easily, such as removing, resizing, or moving parts. This may help future 3D generation systems become more efficient, controllable, and useful for applications such as robotics, simulation, design, and virtual content creation.