Rethinking 3D Shape Generation: Diffusion over Superquadrics

2026-06-07

AI Summary

Existing 3D generation methods rely on high-dimensional geometric representations—such as voxels, signed distance functions (SDFs), or point clouds—which incur substantial computational and memory costs, making it challenging to simultaneously achieve high resolution and controllability. This work introduces the first diffusion-based approach operating directly in the compact parameter space of superquadrics, representing 3D shapes with only approximately 7 KB of parameters encoding pose, scale, and shape. By drastically reducing the state dimensionality, the method enables resolution-free point cloud decoding, part-level editing, and explicit geometric constraints. It achieves competitive surface fidelity and distribution quality on standard benchmarks, with per-shape generation times consistently under 0.6 seconds.

Abstract

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.

Problem

• 3D shape generation
• diffusion models
• high-cardinality representation
• scalability
• geometric primitives

Innovation

• diffusion models
• superquadrics
• 3D shape generation
• compact representation
• scalable generation