HilbertGen-3D:Hilbert--Multifractal Conditioning for Topology-Aware 3D Generation

High-fidelity 3D generative modeling underpins game asset creation, medical imaging, and VR/AR environmental design, where geometric structure directly influences perception and decision-making. Diffusion models represent a powerful paradigm for point cloud generation, yet existing approaches rely heavily on local voxel or patch features and often miss global structural organization. Recent topology-aware methods show that global conditioning can improve generation quality, yet persistent-homology pipelines add substantial preprocessing complexity. We introduce HilbertGen-3D, a topology-aware conditional diffusion framework based on Hilbert–Multifractal Conditioning (HMC). HMC computes multi-scale voxel measures, serializes them via a 3D Hilbert curve to expose structured spatial dependencies, and estimates the generalized fractal dimensions from scale-dependent partition functions. We encode these signals as global embeddings and multi-scale tokens, and inject them into a diffusion denoiser through an efficient bottleneck fusion module. On ShapeNet dataset, HilbertGen-3D reduces the 1-Nearest Neighbor Accuracy by up to 8.74 points and improves coverage by up to +21.45 over prior topology-aware methods. This shows that combining local density cues with global Hilbert–multifractal structure provides a simple, efficient, and effective recipe for high-fidelity and diverse 3D generation.