# Planar Symmetric Pattern Generation

arXiv: https://arxiv.org/abs/2606.02073 · HTML: https://mlsanity.com/paper/2606.02073/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [VLP: A Survey on Vision-Language Pre-training](https://mlsanity.com/paper/2202.09061/) (2022)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Learning Texture Manifolds with the Periodic Spatial GAN](https://mlsanity.com/paper/1705.06566/) (2017)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Taming Text-to-Sounding Video Generation via Advanced Modality Condition and Interaction](https://mlsanity.com/paper/2510.03117/) (2025)
- [Siamese Foundation Models for Crystal Structure Prediction](https://mlsanity.com/paper/2503.10471/) (2025)
- [Optimization and Generation in Aerodynamics Inverse Design](https://mlsanity.com/paper/2602.03582/) (2026)
- [DMFlow: Disordered Materials Generation by Flow Matching](https://mlsanity.com/paper/2602.04734/) (2026)
- [Topology Optimization with Text-Guided Stylization](https://mlsanity.com/paper/2310.15506/) (2023)
- [MicroDreamer: Efficient 3D Generation in ~20 Seconds by Score-based Iterative Reconstruction](https://mlsanity.com/paper/2404.19525/) (2024)
- [HarmonyCut: Supporting Creative Chinese Paper-cutting Design with Form and Connotation Harmony](https://mlsanity.com/paper/2502.07628/) (2025)

## Abstract (arXiv)

Generating objects with specific symmetries is essential in various real-world scenarios. However, adapting existing 2D continuous representations to enforce planar group symmetry remains a challenge, as the transformation of non-reflective group elements may disrupt continuity. To overcome this limitation, we propose a symmetrization framework for arbitrary planar groups. Our method transforms any 2D continuous representation into a symmetric one while preserving continuity. We provide the mathematical formulation of this representation, demonstrate its approximation capability for symmetric functions, and detail the construction methodology. We validate our approach through three visual design tasks (pattern design, paper-cutting design and stylized topology design) and one material design task. Experiments confirm that our representation enables effective symmetry control and demonstrate its broader applicability.