# Symmetry Matters: Auditing and Symmetrizing 3D Generative Models

arXiv: https://arxiv.org/abs/2512.18953 · HTML: https://mlsanity.com/paper/2512.18953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Portrait Shadow Manipulation](https://mlsanity.com/paper/2005.08925/) (2020)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [Learning Part Generation and Assembly for Structure-aware Shape Synthesis](https://mlsanity.com/paper/1906.06693/) (2019)
- [Symmetry and Uncertainty-Aware Object SLAM for 6DoF Object Pose Estimation](https://mlsanity.com/paper/2205.01823/) (2022)
- [Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry](https://mlsanity.com/paper/2007.13393/) (2020)
- [NeRD: Neural 3D Reflection Symmetry Detector](https://mlsanity.com/paper/2105.03211/) (2021)
- [An Adjustable Farthest Point Sampling Method for Approximately-sorted Point Cloud Data](https://mlsanity.com/paper/2208.08795/) (2022)
- [Robust Symmetry Detection via Riemannian Langevin Dynamics](https://mlsanity.com/paper/2410.02786/) (2024)
- [A Generative Model of Symmetry Transformations](https://mlsanity.com/paper/2403.01946/) (2024)
- [AutoSweep: Recovering 3D Editable Objectsfrom a Single Photograph](https://mlsanity.com/paper/2005.13312/) (2020)
- [Efficient and Scalable Point Cloud Generation with Sparse Point-Voxel Diffusion Models](https://mlsanity.com/paper/2408.06145/) (2024)
- [Object-Centric Multi-View Aggregation](https://mlsanity.com/paper/2007.10300/) (2020)
- [SYM3D: Learning Symmetric Triplanes for Better 3D-Awareness of GANs](https://mlsanity.com/paper/2406.06432/) (2024)
- [SeaLion: Semantic Part-Aware Latent Point Diffusion Models for 3D Generation](https://mlsanity.com/paper/2505.17721/) (2025)
- [Geometric Generative Models based on Morphological Equivariant PDEs and GANs](https://mlsanity.com/paper/2403.14897/) (2024)

## Abstract (arXiv)

Symmetry is a strong prior present in many object categories, yet standard benchmarks for 3D generative models rarely report whether this prior is preserved. We study symmetry preservation in unconditional point cloud generation. We first audit the symmetry of generated shapes by several 3D generative models and compute a normalized symmetry score based on the Chamfer Distance (CD). We show that although current 3D generative models achieve competitive results under standard evaluation, they reveal a persistent symmetry gap when a symmetry-aware evaluation protocol is applied. To test whether this gap is merely inherited from the training data, we evaluate these models over a mirrored-objects dataset derived from ShapeNet and analyze symmetry dynamics during training. Mechanism-inspired diagnostic tests were conducted at the sampling and latent-representation levels to further show that reflection symmetry is not reliably encoded in the learned generative process. Finally, to address this gap, we propose a data-centric symmetry-based intervention: training generative models on a half-objects dataset and reconstructing full objects by reflection during sampling. Across multiple backbones, this intervention substantially improves geometric consistency and visual plausibility while remaining competitive under standard metrics. These findings suggest that symmetry-aware evaluation is needed alongside standard benchmarks, and future 3D generative models should incorporate this prior explicitly, either during training or sampling.