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

arXiv: https://arxiv.org/abs/2503.02161 · HTML: https://mlsanity.com/paper/2503.02161/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 32 of its 55 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 32)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [TabLLM: Few-shot Classification of Tabular Data with Large Language Models](https://mlsanity.com/paper/2210.10723/) (2022)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Why Tabular Foundation Models Should Be a Research Priority](https://mlsanity.com/paper/2405.01147/) (2024)
- [REaLTabFormer: Generating Realistic Relational and Tabular Data using Transformers](https://mlsanity.com/paper/2302.02041/) (2023)
- [STaSy: Score-based Tabular data Synthesis](https://mlsanity.com/paper/2210.04018/) (2022)
- [CoDi: Co-evolving Contrastive Diffusion Models for Mixed-type Tabular Synthesis](https://mlsanity.com/paper/2304.12654/) (2023)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [CTAB-GAN+: Enhancing Tabular Data Synthesis](https://mlsanity.com/paper/2204.00401/) (2022)
- [TabuLa: Harnessing Language Models for Tabular Data Synthesis](https://mlsanity.com/paper/2310.12746/) (2023)
- [FinDiff: Diffusion Models for Financial Tabular Data Generation](https://mlsanity.com/paper/2309.01472/) (2023)
- [Rethinking Tabular Data Understanding with Large Language Models](https://mlsanity.com/paper/2312.16702/) (2023)
- [Scaling While Privacy Preserving: A Comprehensive Synthetic Tabular Data Generation and Evaluation in Learning Analytics](https://mlsanity.com/paper/2401.06883/) (2024)
- [HARMONIC: Harnessing LLMs for Tabular Data Synthesis and Privacy Protection](https://mlsanity.com/paper/2408.02927/) (2024)
- [TabEBM: A Tabular Data Augmentation Method with Distinct Class-Specific Energy-Based Models](https://mlsanity.com/paper/2409.16118/) (2024)
- [Enhancing Supply Chain Visibility with Knowledge Graphs and Large Language Models](https://mlsanity.com/paper/2408.07705/) (2024)
- [On Implementing Autonomous Supply Chains: a Multi-Agent System Approach](https://mlsanity.com/paper/2310.09435/) (2023)
- [LaTable: Towards Large Tabular Models](https://mlsanity.com/paper/2406.17673/) (2024)
- [Optimization Techniques for Unsupervised Complex Table Reasoning via Self-Training Framework](https://mlsanity.com/paper/2212.10097/) (2022)
- [Towards Autonomous Supply Chains: Definition, Characteristics, Conceptual Framework, and Autonomy Levels](https://mlsanity.com/paper/2401.14183/) (2023)

## Built on by (most cited first, 9 of 9)

- [A Survey on Evaluating Quality and Trustworthiness in LLM-Generated Data](https://mlsanity.com/paper/2601.17717/) (2026)
- [Dependency-aware synthetic tabular data generation](https://mlsanity.com/paper/2507.19211/) (2025)
- [Measuring the Dependency Gap: Diagnosing Inter-Column Fidelity in Tabular Generative Models](https://mlsanity.com/paper/2607.21636/) (2026)
- [A Note on Statistically Accurate Tabular Data Generation Using Large Language Models](https://mlsanity.com/paper/2505.02659/) (2025)
- [SynDelay: A Synthetic Dataset for Delivery Delay Prediction](https://mlsanity.com/paper/2509.05325/) (2025)
- [Declarative Outcome-Conformant Synthesis: Exact, Closed-Form Specification Satisfaction and a Conformance Benchmark](https://mlsanity.com/paper/2606.08736/) (2026)
- [LAB-Tab: LLM-Augmented Bayesian Network Adaptation for Few-Shot Tabular Generation](https://mlsanity.com/paper/2608.01879/) (2026)
- [Constraint-Aware Synthetic Tabular Data Generation via Inter-Column Constraint Discovery with LLM Agents](https://mlsanity.com/paper/2608.15109/) (2026)
- [Scalable extraction and visualization of multi-attribute logical and functional dependencies in tabular data](https://mlsanity.com/paper/2610.08287/) (2026)

## Abstract (arXiv)

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.