# CausalWrap: Model-Agnostic Causal Constraint Wrappers for Tabular Synthetic Data

arXiv: https://arxiv.org/abs/2603.02015 · HTML: https://mlsanity.com/paper/2603.02015/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [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)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data](https://mlsanity.com/paper/2402.04823/) (2024)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Physics-informed deep generative models](https://mlsanity.com/paper/1812.03511/) (2018)
- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (2024)
- [Causal-TGAN: Generating Tabular Data Using Causal Generative Adversarial Networks](https://mlsanity.com/paper/2104.10680/) (2021)
- [TabStruct: Measuring Structural Fidelity of Tabular Data](https://mlsanity.com/paper/2509.11950/) (2025)
- [Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework](https://mlsanity.com/paper/2406.08311/) (2024)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Achieving Constraints in Neural Networks: A Stochastic Augmented Lagrangian Approach](https://mlsanity.com/paper/2310.16647/) (2023)
- [Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inference](https://mlsanity.com/paper/2510.18768/) (2025)
- [Generating Synthetic Relational Tabular Data via Structural Causal Models](https://mlsanity.com/paper/2507.03528/) (2025)

## Built on by (most cited first, 2 of 2)

- [Workload-Preserving Differentially Private Synthetic Data for Causal Inference via Maximum-Entropy Calibration](https://mlsanity.com/paper/2607.08122/) (2026)
- [Beyond Distributional Fidelity: Causal-Penalized Diffusion for Synthetic Tabular Data](https://mlsanity.com/paper/2610.11407/) (2026)

## Abstract (arXiv)

Tabular synthetic data generators are typically trained to match observational distributions, which can yield high conventional utility (e.g., column correlations, predictive accuracy) yet poor preservation of structural relations relevant to causal analysis and out-of-distribution (OOD) reasoning. When the downstream use of synthetic data involves causal reasoning -- estimating treatment effects, evaluating policies, or testing mediation pathways -- merely matching the observational distribution is insufficient: structural fidelity and treatment-mechanism preservation become essential. We propose CausalWrap (CW), a model-agnostic wrapper that injects partial causal knowledge (PCK) -- trusted edges, forbidden edges, and qualitative/monotonic constraints -- into any pretrained base generator (GAN, VAE, or diffusion model), without requiring access to its internals. CW learns a lightweight, differentiable post-hoc correction map applied to samples from the base generator, optimized with causal penalty terms under an augmented-Lagrangian schedule. We provide theoretical results connecting penalty-based optimization to constraint satisfaction and relating approximate factorization to joint distributional control. We validate CW on simulated structural causal models (SCMs) with known ground-truth interventions, semi-synthetic causal benchmarks (IHDP and an ACIC-style suite), and a real-world ICU cohort (MIMIC-IV) with expert-elicited partial graphs. CW improves causal fidelity across diverse base generators -- e.g., reducing average treatment effect (ATE) error by up to 63% on ACIC and lifting ATE agreement from 0.00 to 0.38 on the intensive care unit (ICU) cohort -- while largely retaining conventional utility.