# Statistical Guarantees in Synthetic Data through Conformal Adversarial Generation

arXiv: https://arxiv.org/abs/2504.17058 · HTML: https://mlsanity.com/paper/2504.17058/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Risk-Aware and Explainable Framework for Ensuring Guaranteed Coverage in Evolving Hardware Trojan Detection](https://mlsanity.com/paper/2312.00009/) (2023)
- [Chatting with Logs: An exploratory study on Finetuning LLMs for LogQL](https://mlsanity.com/paper/2412.03612/) (2024)

## Abstract (arXiv)

The generation of high-quality synthetic data presents significant challenges in machine learning research, particularly regarding statistical fidelity and uncertainty quantification. Existing generative models produce compelling synthetic samples but lack rigorous statistical guarantees about their relation to the underlying data distribution, limiting their applicability in critical domains requiring robust error bounds. We address this fundamental limitation by presenting a novel framework that incorporates conformal prediction methodologies into Generative Adversarial Networks (GANs). By integrating multiple conformal prediction paradigms including Inductive Conformal Prediction (ICP), Mondrian Conformal Prediction, Cross-Conformal Prediction, and Venn-Abers Predictors, we establish distribution-free uncertainty quantification in generated samples. This approach, termed Conformalized GAN (cGAN), demonstrates enhanced calibration properties while maintaining the generative power of traditional GANs, producing synthetic data with provable statistical guarantees. We provide rigorous mathematical proofs establishing finite-sample validity guarantees and asymptotic efficiency properties, enabling the reliable application of synthetic data in high-stakes domains including healthcare, finance, and autonomous systems.