# GeoLoom: High-quality Geometric Diagram Generation from Textual Input

arXiv: https://arxiv.org/abs/2512.08180 · HTML: https://mlsanity.com/paper/2512.08180/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 30 of 33)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [Muse: Text-To-Image Generation via Masked Generative Transformers](https://mlsanity.com/paper/2301.00704/) (2023)
- [StackGAN: Text to Photo-realistic Image Synthesis with Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1612.03242/) (2016)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Evaluating Text-to-Visual Generation with Image-to-Text Generation](https://mlsanity.com/paper/2404.01291/) (2024)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [LLM-grounded Diffusion: Enhancing Prompt Understanding of Text-to-Image Diffusion Models with Large Language Models](https://mlsanity.com/paper/2305.13655/) (2023)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [DeepSVG: A Hierarchical Generative Network for Vector Graphics Animation](https://mlsanity.com/paper/2007.11301/) (2020)
- [Seedream 3.0 Technical Report](https://mlsanity.com/paper/2504.11346/) (2025)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [A Learned Representation for Scalable Vector Graphics](https://mlsanity.com/paper/1904.02632/) (2019)
- [FlowAR: Scale-wise Autoregressive Image Generation Meets Flow Matching](https://mlsanity.com/paper/2412.15205/) (2024)
- [AutomaTikZ: Text-Guided Synthesis of Scientific Vector Graphics with TikZ](https://mlsanity.com/paper/2310.00367/) (2023)
- [IconShop: Text-Guided Vector Icon Synthesis with Autoregressive Transformers](https://mlsanity.com/paper/2304.14400/) (2023)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Orthus: Autoregressive Interleaved Image-Text Generation with Modality-Specific Heads](https://mlsanity.com/paper/2412.00127/) (2024)
- [Chat2SVG: Vector Graphics Generation with Large Language Models and Image Diffusion Models](https://mlsanity.com/paper/2411.16602/) (2024)
- [From Words to Structured Visuals: A Benchmark and Framework for Text-to-Diagram Generation and Editing](https://mlsanity.com/paper/2411.11916/) (2024)
- [DiagrammerGPT: Generating Open-Domain, Open-Platform Diagrams via LLM Planning](https://mlsanity.com/paper/2310.12128/) (2023)
- [NeuralSVG: An Implicit Representation for Text-to-Vector Generation](https://mlsanity.com/paper/2501.03992/) (2025)

## Built on by (most cited first, 2 of 2)

- [Math-Vision Diagrams: A Comprehensive Benchmark for Evaluating LLM Mathematical Diagram Generation Capabilities](https://mlsanity.com/paper/2608.08964/) (2026)
- [MathVis: Can AI Reason through Drawing? A Benchmark for Mathematical Figure Generation](https://mlsanity.com/paper/2610.12954/) (2026)

## Abstract (arXiv)

High-quality geometric diagram generation presents both a challenge and an opportunity: it demands strict spatial accuracy while offering well-defined constraints to guide generation. Inspired by recent advances in geometry problem solving that employ formal languages and symbolic solvers for enhanced correctness and interpretability, we propose GeoLoom, a novel framework for text-to-diagram generation in geometric domains. GeoLoom comprises two core components: an autoformalization module that translates natural language into a specifically designed generation-oriented formal language GeoLingua, and a coordinate solver that maps formal constraints to precise coordinates using the efficient Monte Carlo optimization. To support this framework, we introduce GeoNF, a dataset aligning natural language geometric descriptions with formal GeoLingua descriptions. We further propose a constraint-based evaluation metric that quantifies structural deviation, offering mathematically grounded supervision for iterative refinement. Empirical results demonstrate that GeoLoom significantly outperforms state-of-the-art baselines in structural fidelity, providing a principled foundation for interpretable and scalable diagram generation.