# How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data

arXiv: https://arxiv.org/abs/2402.04823 · HTML: https://mlsanity.com/paper/2402.04823/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 56 references that are in the map.
- First posted on arXiv 7 Feb 2024.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Generating Multi-label Discrete Patient Records using Generative Adversarial Networks](https://mlsanity.com/paper/1703.06490/) (2017)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [CTAB-GAN: Effective Table Data Synthesizing](https://mlsanity.com/paper/2102.08369/) (2021)
- [DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networks](https://mlsanity.com/paper/2110.12884/) (2021)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [STaSy: Score-based Tabular data Synthesis](https://mlsanity.com/paper/2210.04018/) (2022)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [Boosting Deep Learning Risk Prediction with Generative Adversarial Networks for Electronic Health Records](https://mlsanity.com/paper/1709.01648/) (2017)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Efficient Generation of Structured Objects with Constrained Adversarial Networks](https://mlsanity.com/paper/2007.13197/) (2020)
- [OCT-GAN: Neural ODE-based Conditional Tabular GANs](https://mlsanity.com/paper/2105.14969/) (2021)
- [Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesis](https://mlsanity.com/paper/2202.03636/) (2022)
- [A Unified Framework for Adversarial Attack and Defense in Constrained Feature Space](https://mlsanity.com/paper/2112.01156/) (2021)
- [Generating Multi-Categorical Samples with Generative Adversarial Networks](https://mlsanity.com/paper/1807.01202/) (2018)

## Built on by (most cited first, 29 of 29)

- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints](https://mlsanity.com/paper/2502.18237/) (2025)
- [ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection](https://mlsanity.com/paper/2502.06774/) (2025)
- [Tabular Data Augmentation for Machine Learning: Progress and Prospects of Embracing Generative AI](https://mlsanity.com/paper/2407.21523/) (2024)
- [A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond](https://mlsanity.com/paper/2503.05954/) (2025)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction](https://mlsanity.com/paper/2503.19466/) (2025)
- [TabularBench: Benchmarking Adversarial Robustness for Tabular Deep Learning in Real-world Use-cases](https://mlsanity.com/paper/2408.07579/) (2024)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [Logic Tensor Network-Enhanced Generative Adversarial Network](https://mlsanity.com/paper/2601.03839/) (2026)
- [PiShield: A PyTorch Package for Learning with Requirements](https://mlsanity.com/paper/2402.18285/) (2024)
- [CausalWrap: Model-Agnostic Causal Constraint Wrappers for Tabular Synthetic Data](https://mlsanity.com/paper/2603.02015/) (2026)
- [Deep generative models as an adversarial attack strategy for tabular machine learning](https://mlsanity.com/paper/2409.12642/) (2024)
- [Deep Generative Models with Hard Linear Equality Constraints](https://mlsanity.com/paper/2502.05416/) (2025)
- [Exact Synthetic Populations for Scalable Societal and Market Modeling](https://mlsanity.com/paper/2512.07306/) (2025)
- [ReTabSyn: Realistic Tabular Data Synthesis via Reinforcement Learning](https://mlsanity.com/paper/2603.10823/) (2026)
- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [Generating Reliable Synthetic Clinical Trial Data: The Role of Hyperparameter Optimization and Domain Constraints](https://mlsanity.com/paper/2505.05019/) (2025)
- [Constraint-Guided Prediction Refinement via Deterministic Diffusion Trajectories](https://mlsanity.com/paper/2506.12911/) (2025)
- [Insights on Adversarial Attacks for Tabular Machine Learning via a Systematic Literature Review](https://mlsanity.com/paper/2506.15506/) (2025)
- [Limited Reference, Reliable Generation: A Two-Component Framework for Tabular Data Generation in Low-Data Regimes](https://mlsanity.com/paper/2509.09960/) (2025)
- [Harpoon: Generalised Manifold Guidance for Conditional Tabular Diffusion](https://mlsanity.com/paper/2602.07875/) (2026)
- [Stable and Privacy-Preserving Synthetic Educational Data with Empirical Marginals: A Copula-Based Approach](https://mlsanity.com/paper/2604.04195/) (2026)
- [CAffNet: Hard Constraint-Affine Neural Networks](https://mlsanity.com/paper/2605.24437/) (2026)
- [Neural Slack Variables for Shape Constraints](https://mlsanity.com/paper/2606.13803/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)
- [Constraint-Aware Synthetic Tabular Data Generation via Inter-Column Constraint Discovery with LLM Agents](https://mlsanity.com/paper/2608.15109/) (2026)
- [Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs](https://mlsanity.com/paper/2608.21605/) (2026)

## Abstract (arXiv)

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding 95% non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to 6.5% improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.