LLM-TabLogic: Preserving Inter-Column Logical Relationships in Synthetic Tabular Data via Prompt-Guided Latent Diffusion

Synthetic tabular data are increasingly being used to replace real data, serving as an effective solution that simultaneously protects privacy and addresses data scarcity. However, in addition to preserving global statistical properties, synthetic datasets must also maintain domain-specific logical consistency**-**especially in complex systems like supply chains, where fields such as shipment dates, locations, and product categories must remain logically consistent for real-world usability. Existing generative models often overlook these inter-column relationships, leading to unreliable synthetic tabular data in real-world applications. To address these challenges, we propose LLM-TabLogic, a novel approach that leverages Large Language Model reasoning to capture and compress the complex logical relationships among tabular columns, while these conditional constraints are passed into a Score-based Diffusion model for data generation in latent space. Through extensive experiments on real-world industrial datasets, we evaluate LLM-TabLogic for column reasoning and data generation, comparing it with five baselines including SMOTE and state-of-the-art generative models. Our results show that LLM-TabLogic demonstrates strong generalization in logical inference, achieving over 90% accuracy on unseen tables. Furthermore, our method outperforms all baselines in data generation by fully preserving inter-column relationships while maintaining the best balance between data fidelity, utility, and privacy. This study presents the first method to effectively preserve inter-column relationships in synthetic tabular data generation without requiring domain knowledge, offering new insights for creating logically consistent real-world tabular data. The code is available at https://github.com/Yunbo-max/TabKG.