# Denoising Functional Maps: Diffusion Models for Shape Correspondence

arXiv: https://arxiv.org/abs/2503.01845 · HTML: https://mlsanity.com/paper/2503.01845/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 43 of its 76 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## 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 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)
- [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020)
- [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)

## Built on by (most cited first, 14 of 14)

- [Hierarchical Neural Semantic Representation for 3D Semantic Correspondence](https://mlsanity.com/paper/2509.17431/) (2025)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [L3DR: 3D-aware LiDAR Diffusion and Rectification](https://mlsanity.com/paper/2602.19064/) (2026)
- [SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization](https://mlsanity.com/paper/2603.12937/) (2026)
- [DcMatch: Unsupervised Multi-Shape Matching with Dual-Level Consistency](https://mlsanity.com/paper/2509.01204/) (2025)
- [SemMorph3D: Unsupervised Semantic-Aware 3D Morphing via Mesh-Guided Gaussians](https://mlsanity.com/paper/2510.02034/) (2025)
- [SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signals](https://mlsanity.com/paper/2605.18039/) (2026)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [Ordered Diffusion for 3D Human Registration](https://mlsanity.com/paper/2608.05804/) (2026)
- [Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach](https://mlsanity.com/paper/2509.06862/) (2025)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)
- [GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models](https://mlsanity.com/paper/2607.00492/) (2026)
- [MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence](https://mlsanity.com/paper/2607.15887/) (2026)
- [TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation](https://mlsanity.com/paper/2609.04202/) (2026)

## Abstract (arXiv)

Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page for the source code and the datasets.