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arXiv · 2512.08180

GeoLoom: High-quality Geometric Diagram Generation from Textual Input

Xiaojing Wei·Ting Zhang·Wei He·Jingdong Wang·Hua Huang
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Abstract

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.

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Xiaojing Wei, Ting Zhang, Wei He, Jingdong Wang, Hua Huang. 2026-06-09. GeoLoom: High-quality Geometric Diagram Generation from Textual Input. https://arxiv.org/abs/2512.08180

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