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.

本研究提出了GeoUni，首个统一的几何专家模型，能够在单一框架内生成问题解决方案和图形。这一模型填补了机器学习中处理几何问题和图形生成的空白，展示了在几何推理任务中与更大规模模型相当的表现，并能够依据特定知识点成功生成匹配的文本问题及图形，极大地拓展了模型的能力。 

GeoUni: 生成几何图形、问题及问题解决方案的统一模型