Constraint-Aware Synthetic Tabular Data Generation via Inter-Column Constraint Discovery with LLM Agents

Synthetic data generation is dominated by the fit-then-sample paradigm: a generative model is trained on a private dataset and then sampled from. Despite its widespread adoption, this paradigm faces three challenges: (1) a new training run is required for every dataset; (2) different data modalities, such as single tables, time series, and relational databases, require task-specific models and feature engineering; and (3) the resulting model is opaque, making its behavior under data constraints difficult to inspect. We propose GENSCRIPT, an inference-only pipeline that eliminates model training. GENSCRIPT computes a deterministic statistical profile of the source data (column types, ranges, missingness, categories, correlations, etc.) and passes it--rather than raw rows--to a language model to infer field semantics and cross-column integrity constraints. A coding agent then compiles the profile and constraints into an executable, auditable sampler. This unified approach supports single-table, temporal, and relational data without task-specific modeling. Across four single-table benchmarks, GENSCRIPT builds generators in 2 minutes and samples 50k rows within 6 seconds, while remaining within a few points of leading methods in marginal fidelity. Notably, it is the only method that perfectly preserves a 1-to-1 mapping between columns in the Adult dataset. On a smart-building dataset, it produces conditional time series that more closely match the real distribution than two baselines and perfectly preserves primary- and foreign-key relationships in the corresponding relational database.

Synthetic tabular data can match real data distributions while still violating the semantic constraints that govern valid tabular rows. This reveals a key limitation of existing tabular generators: they mainly optimize distributional fidelity, but do not explicitly model weak semantic priors encoded in tabular schema and textual descriptions. In this paper, we propose \ours, a semantics-consistent tabular diffusion framework for high-fidelity synthetic data generation under weakly specified semantic priors. \ours\ first constructs two types of priors, namely intra-column semantics and inter-column symbolic rules, with LLM-assisted extraction from metadata and validation on the real training split. These priors are then used as generation conditions rather than post-hoc filters. Specifically, \ours\ maps heterogeneous column values, column identities, and semantic priors into a unified semantic space, and performs column-wise forward corruption and prior-conditioned reverse denoising to preserve both marginal distributions and rule-consistent cross-column dependencies. Extensive experiments on six real-world tabular benchmarks show that \ours\ consistently improves distributional fidelity, semantic consistency, and downstream task utility over representative VAE-, GAN-, LLM-, and diffusion-based baselines. Additional analyses further demonstrate the robustness of \ours\ when semantic priors are partially unavailable.

Deep generative models can help with data scarcity and privacy by producing synthetic training data, but they struggle in low-data, imbalanced tabular settings to fully learn the complex data distribution. We argue that striving for the full joint distribution could be overkill; for greater data efficiency, models should prioritize learning the conditional distribution $P(y\mid \bm{X})$, as suggested by recent theoretical analysis. Therefore, we overcome this limitation with ReTabSyn, a Reinforced Tabular Synthesis pipeline that provides direct feedback on feature correlation preservation during synthesizer training. This objective encourages the generator to prioritize the most useful predictive signals when training data is limited, thereby strengthening downstream model utility. We empirically fine-tune a language model-based generator using this approach, and across benchmarks with small sample sizes, class imbalance, and distribution shift, ReTabSyn consistently outperforms state-of-the-art baselines. Moreover, our approach can be readily extended to control various aspects of synthetic tabular data, such as applying expert-specified constraints on generated observations.