Synthesizing Multimodal Geometry Datasets from Scratch and Enabling Visual Alignment via Plotting Code

Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data and weak visual--symbolic alignment. We propose a pipeline for synthesizing complex multimodal geometry problems from scratch and construct a dataset named \textbf{GeoCode}, which decouples problem generation into symbolic seed construction, grounded instantiation with verification, and code-based diagram rendering, ensuring consistency across structure, text, reasoning, and images. Leveraging the plotting code provided in GeoCode, we further introduce code prediction as an explicit alignment objective, transforming visual understanding into a supervised structured prediction task. GeoCode exhibits substantially higher structural complexity and reasoning difficulty than existing benchmarks, while maintaining mathematical correctness through multi-stage validation. Extensive experiments show that models trained on GeoCode achieve consistent improvements on multiple geometry benchmarks, demonstrating both the effectiveness of the dataset and the proposed alignment strategy.

Geometry problems often require understanding both pictures and mathematical relationships at the same time. Although recent artificial intelligence systems can process images and text together, they still struggle with challenging geometry tasks because they often fail to correctly connect what they see in a diagram with the reasoning needed to solve the problem. Existing training data is also limited in size and complexity. To help address this problem, we created a new way to automatically generate geometry problems and built a dataset called GeoCode. Our method starts from mathematical rules, creates complete problems and solutions, and then generates matching diagrams. This process helps ensure that the questions, images, and answers remain consistent and correct. We also introduce a new training approach that asks AI systems to predict how a geometry diagram was created, rather than only interpreting the final image. This encourages models to better understand the relationship between visual information and the underlying geometric structure. Experiments show that GeoCode contains more complex and challenging problems than existing datasets. AI systems trained with GeoCode perform better on several geometry benchmarks, suggesting that our approach can help build AI systems with stronger visual understanding and reasoning abilities.