# GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutions

arXiv: https://arxiv.org/abs/2504.10146 · HTML: https://mlsanity.com/paper/2504.10146/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [Unified-IO: A Unified Model for Vision, Language, and Multi-Modal Tasks](https://mlsanity.com/paper/2206.08916/) (2022)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [SEED-X: Multimodal Models with Unified Multi-granularity Comprehension and Generation](https://mlsanity.com/paper/2404.14396/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [Making LLaMA SEE and Draw with SEED Tokenizer](https://mlsanity.com/paper/2310.01218/) (2023)
- [Open-MAGVIT2: An Open-Source Project Toward Democratizing Auto-regressive Visual Generation](https://mlsanity.com/paper/2409.04410/) (2024)
- [UniTok: A Unified Tokenizer for Visual Generation and Understanding](https://mlsanity.com/paper/2502.20321/) (2025)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [QLIP: Text-Aligned Visual Tokenization Unifies Auto-Regressive Multimodal Understanding and Generation](https://mlsanity.com/paper/2502.05178/) (2025)
- [GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation](https://mlsanity.com/paper/2406.11503/) (2024)
- [OCR-VQGAN: Taming Text-within-Image Generation](https://mlsanity.com/paper/2210.11248/) (2022)
- [FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving](https://mlsanity.com/paper/2310.18021/) (2023)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver](https://mlsanity.com/paper/2409.04214/) (2024)
- [MagicGeo: Training-Free Text-Guided Geometric Diagram Generation](https://mlsanity.com/paper/2502.13855/) (2025)

## Built on by (most cited first, 11 of 11)

- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines](https://mlsanity.com/paper/2508.06226/) (2025)
- [GeoSDF: Plane Geometry Diagram Synthesis via Signed Distance Field](https://mlsanity.com/paper/2506.13492/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Do Multi-Agents Solve Better Than Single? Evaluating Agentic Frameworks for Diagram-Grounded Geometry Problem Solving and Reasoning](https://mlsanity.com/paper/2512.16698/) (2025)
- [GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving](https://mlsanity.com/paper/2602.08524/) (2026)
- [Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models](https://mlsanity.com/paper/2604.00890/) (2026)
- [Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving](https://mlsanity.com/paper/2601.21164/) (2026)
- [VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification](https://mlsanity.com/paper/2606.14176/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [Solving Is Not Drawing: A Benchmark for Diagrammatic Reasoning in Olympiad Geometry](https://mlsanity.com/paper/2608.18111/) (2026)

## Abstract (arXiv)

We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally, solving geometry problems and generating diagrams have been treated as separate tasks in machine learning, with no models successfully integrating both to support problem creation. However, we believe that mastery in geometry requires frictionless integration of all of these skills, from solving problems to visualizing geometric relationships, and finally, crafting tailored problems. Our extensive experiments demonstrate that GeoUni, with only 1.5B parameters, achieves performance comparable to larger models such as DeepSeek-R1 with 671B parameters in geometric reasoning tasks. GeoUni also excels in generating precise geometric diagrams, surpassing both text-to-image models and unified models, including the GPT-4o image generation. Most importantly, GeoUni is the only model capable of successfully generating textual problems with matching diagrams based on specific knowledge points, thus offering a wider range of capabilities that extend beyond current models.