ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learning

2026-06-05

AI Summary

Learning a continuous generative space for deformable shapes is highly challenging in the absence of large-scale 3D training data. To address this, this work proposes ARAPDiffusion, a latent diffusion model that incorporates an as-rigid-as-possible (ARAP) regularization term. By integrating ARAP energy as a geometric prior into the diffusion process, the method leverages an implicit decoder to handle unstructured point clouds and jointly optimizes the encoder, decoder, and diffusion model, thereby substantially reducing reliance on extensive training data. Experimental results demonstrate that ARAPDiffusion outperforms existing baselines in both unconditional and conditional shape generation tasks, achieving notable improvements in generation quality and generalization capability.

Abstract

This paper introduces ARAPDiffusion, a latent diffusion model to learn the underlying continuous shape space of a deformation shape collection. The key innovation is in injecting the as-rigid-as-possible (ARAP) deformation model as regularization losses into latent diffusion (LD), releasing the requirement of having abundant 3D training data for learning generative models. In contrast to the standard LD, we show how the ARAP model can be used to improve both the encoder/decoder and the LD model. The training procedure alternates between using the synthetic distribution defined by the LD model to develop a regularization loss that enhances the shape encoder/decoder and using the shape decoder to develop a regularization loss to improve the LD model. We also show the benefit of the LD paradigm in combining a representation-free LD process and an implicit shape decoder that is applicable to unorganized point clouds. The experimental results of unconditional and conditional shape generation demonstrate the advantages of ARAPDiffusion over baseline approaches.

Problem

• shape space learning
• deformable shapes
• 3D generative modeling
• data-efficient learning
• latent diffusion

Innovation

• ARAP regularization
• latent diffusion
• deformable shape space
• implicit shape decoder
• point cloud generation