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

Deformable 3D shapes can undergo large changes in pose and morphology while still preserving plausible local geometry, yet generative models often produce samples with unnatural stretching or distortion. In latent generative models, such failures can arise from two coupled sources: the decoder determines the geometry produced at a latent code, while the generative distribution determines which latent regions are actually visited. We introduce ARAPDiffusion, a latent generative framework that establishes feedback between deformation geometry and the generative distribution. First, latent codes sampled from the current diffusion model determine where as-rigid-as-possible (ARAP) constraint is applied, concentrating geometric supervision in regions that the generator actually visits. Second, generated shapes are evaluated by their deformation relative to the observed shape family, and these scores modulate the influence of generated samples during diffusion refinement. In this way, the generative distribution determines where geometry is enforced, while deformation quality in turn reshapes what the model generates. ARAPDiffusion applies to both consistently meshed shapes and unordered point clouds, and the learned prior can also be used for conditional reconstruction. Experiments across human, animal, and bone shape families show consistent improvements in generated-shape quality, distribution matching, and reconstruction accuracy.