{"ID":2830978,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08180","arxiv_id":"2512.08180","title":"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.","short_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 i...","url_abs":"https://arxiv.org/abs/2512.08180","url_pdf":"https://arxiv.org/pdf/2512.08180v1","authors":"[\"Xiaojing Wei\",\"Ting Zhang\",\"Wei He\",\"Jingdong Wang\",\"Hua Huang\"]","published":"2025-12-09T02:22:23Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false}