# Robust Symmetry Detection via Riemannian Langevin Dynamics

arXiv: https://arxiv.org/abs/2410.02786 · HTML: https://mlsanity.com/paper/2410.02786/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [AnimateDiff: Animate Your Personalized Text-to-Image Diffusion Models without Specific Tuning](https://mlsanity.com/paper/2307.04725/) (2023)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Latent Video Diffusion Models for High-Fidelity Long Video Generation](https://mlsanity.com/paper/2211.13221/) (2022)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Portrait Shadow Manipulation](https://mlsanity.com/paper/2005.08925/) (2020)
- [Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry](https://mlsanity.com/paper/2007.13393/) (2020)
- [PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models](https://mlsanity.com/paper/1910.06511/) (2019)
- [NeRD: Neural 3D Reflection Symmetry Detector](https://mlsanity.com/paper/2105.03211/) (2021)
- [AutoSweep: Recovering 3D Editable Objectsfrom a Single Photograph](https://mlsanity.com/paper/2005.13312/) (2020)
- [Object-Centric Multi-View Aggregation](https://mlsanity.com/paper/2007.10300/) (2020)
- [SymmetryNet: Learning to Predict Reflectional and Rotational Symmetries of 3D Shapes from Single-View RGB-D Images](https://mlsanity.com/paper/2008.00485/) (2020)

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

- [PDT: Point Distribution Transformation with Diffusion Models](https://mlsanity.com/paper/2507.18939/) (2025)
- [Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation](https://mlsanity.com/paper/2411.17763/) (2024)
- [Splat and Replace: 3D Reconstruction with Repetitive Elements](https://mlsanity.com/paper/2506.06462/) (2025)
- [FRIDU: Functional Map Refinement with Guided Image Diffusion](https://mlsanity.com/paper/2506.14322/) (2025)
- [Symmetry Understanding of 3D Shapes via Chirality Disentanglement](https://mlsanity.com/paper/2508.05505/) (2025)
- [Axis-level Symmetry Detection with Group-Equivariant Representation](https://mlsanity.com/paper/2508.10740/) (2025)
- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [Mean-Shift Distillation for Diffusion Mode Seeking](https://mlsanity.com/paper/2502.15989/) (2025)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)
- [Quantum-Inspired Harmonic Decision Models: A Computational Framework for Music Generation](https://mlsanity.com/paper/2607.05007/) (2026)
- [Training-free zero-shot 3D symmetry detection with visual features back-projected to geometry](https://mlsanity.com/paper/2505.24162/) (2025)
- [Symmetry Matters: Auditing and Symmetrizing 3D Generative Models](https://mlsanity.com/paper/2512.18953/) (2025)
- [ArchSym: Detecting 3D-Grounded Architectural Symmetries in the Wild](https://mlsanity.com/paper/2604.22202/) (2026)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

Symmetries are ubiquitous across all kinds of objects, whether in nature or in man-made creations. While these symmetries may seem intuitive to the human eye, detecting them with a machine is nontrivial due to the vast search space. Classical geometry-based methods work by aggregating "votes" for each symmetry but struggle with noise. In contrast, learning-based methods may be more robust to noise, but often overlook partial symmetries due to the scarcity of annotated data. In this work, we address this challenge by proposing a novel symmetry detection method that marries classical symmetry detection techniques with recent advances in generative modeling. Specifically, we apply Langevin dynamics to a redefined symmetry space to enhance robustness against noise. We provide empirical results on a variety of shapes that suggest our method is not only robust to noise, but can also identify both partial and global symmetries. Moreover, we demonstrate the utility of our detected symmetries in various downstream tasks, such as compression and symmetrization of noisy shapes.