GeoLoom: High-quality Geometric Diagram Generation from Textual Input
This addresses the challenge of accurate geometric diagram generation for applications requiring strict spatial constraints, though it appears incremental by building on existing formal language and optimization techniques.
The paper tackles the problem of generating high-quality geometric diagrams from textual input by proposing GeoLoom, a framework that translates natural language into a formal language and solves coordinates via Monte Carlo optimization. It significantly outperforms state-of-the-art baselines in structural fidelity, as demonstrated empirically.
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.