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

arXiv: https://arxiv.org/abs/2606.06887 · HTML: https://mlsanity.com/paper/2606.06887/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 37 of its 46 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Hunyuan3D 2.5: Towards High-Fidelity 3D Assets Generation with Ultimate Details](https://mlsanity.com/paper/2506.16504/) (2025)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Unsupervised Shape and Pose Disentanglement for 3D Meshes](https://mlsanity.com/paper/2007.11341/) (2020)
- [Estimating Body and Hand Motion in an Ego-sensed World](https://mlsanity.com/paper/2410.03665/) (2024)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [RoHM: Robust Human Motion Reconstruction via Diffusion](https://mlsanity.com/paper/2401.08570/) (2024)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Score-Guided Diffusion for 3D Human Recovery](https://mlsanity.com/paper/2403.09623/) (2024)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [Frame Averaging for Equivariant Shape Space Learning](https://mlsanity.com/paper/2112.01741/) (2021)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [GLASS: Geometric Latent Augmentation for Shape Spaces](https://mlsanity.com/paper/2108.03225/) (2021)
- [DPoser-X: Diffusion Model as Robust 3D Whole-body Human Pose Prior](https://mlsanity.com/paper/2508.00599/) (2025)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)

## Abstract (arXiv)

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.