GeoLoom: High-quality Geometric Diagram Generation from Textual Input

• URL: http://arxiv.org/abs/2512.08180v1
• Date: Tue, 09 Dec 2025 02:22:23 GMT
• Title: GeoLoom: High-quality Geometric Diagram Generation from Textual Input
• Authors: Xiaojing Wei, Ting Zhang, Wei He, Jingdong Wang, Hua Huang,
• Abstract summary: We propose GeoLoom, a novel framework for text-to-diagram generation in geometric domains.<n>GeoLoom comprises two core components: an autoformalization module that translates natural language into a generation-oriented formal language GeoLingua.<n>To support this framework, we introduce GeoNF, a dataset aligning natural language geometric descriptions with formal GeoLingua descriptions.
• Score: 41.9055060542649
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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