DoubleDiffusion: Combining Heat Diffusion with Denoising Diffusion for Generative Learning on 3D Meshes

2025-01-06

AI Summary

Generating continuous textures (e.g., RGB images) directly on 3D mesh surfaces remains challenging, as existing approaches rely on mesh parameterization or implicit representations—both prone to geometric distortion and fidelity loss. This paper introduces the first probabilistic generative framework that jointly leverages heat diffusion (governed by the Laplacian–Beltrami operator) and denoising diffusion to model texture signals on non-Euclidean manifolds while preserving intrinsic geometric structure. Unlike prior methods, it operates directly on mesh topology without parameterization or implicit fields, enabling topology-aware feature propagation and shape-conditioned texture synthesis. Experiments demonstrate high-fidelity, geometry-consistent RGB texture generation on complex surfaces. Notably, our method achieves, for the first time, category-level conditional texture synthesis across diverse shapes—marking a paradigm shift in 3D asset generation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

This paper proposes DoubleDiffusion, a novel framework that combines heat dissipation diffusion and denoising diffusion for direct generative learning on 3D mesh surfaces. Our approach addresses the challenges of generating continuous signal distributions residing on a curve manifold surface. Unlike previous methods that rely on unrolling 3D meshes into 2D or adopting field representations, DoubleDiffusion leverages the Laplacian-Beltrami operator to process features respecting the mesh structure. This combination enables effective geometry-aware signal diffusion across the underlying geometry. As shown in Fig.~ ef{fig:teaser}, we demonstrate that DoubleDiffusion has the ability to generate RGB signal distributions on complex 3D mesh surfaces and achieves per-category shape-conditioned texture generation across different shape geometry. Our work contributes a new direction in diffusion-based generative modeling on 3D surfaces, with potential applications in the field of 3D asset generation.

Problem

• 3D Mesh
• Continuous Image Generation
• Geometric Preservation

Innovation

• DoubleDiffusion
• 3D mesh generation
• Laplace-Beltrami operator