GeoLoom: High-quality Geometric Diagram Generation from Textual Input

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.