# Privacy Amplification Persists under Unlimited Synthetic Data Release

arXiv: https://arxiv.org/abs/2602.04895 · HTML: https://mlsanity.com/paper/2602.04895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 3 Feb 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Differentially Private Diffusion Models](https://mlsanity.com/paper/2210.09929/) (2022)
- [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021)
- [Privacy Amplification by Iteration](https://mlsanity.com/paper/1808.06651/) (2018)
- [Model Collapse Demystified: The Case of Regression](https://mlsanity.com/paper/2402.07712/) (2024)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [Efficient Private ERM for Smooth Objectives](https://mlsanity.com/paper/1703.09947/) (2017)
- [Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Loss](https://mlsanity.com/paper/2205.13710/) (2022)
- [TAPAS: a Toolbox for Adversarial Privacy Auditing of Synthetic Data](https://mlsanity.com/paper/2211.06550/) (2022)
- ["What do you want from theory alone?" Experimenting with Tight Auditing of Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2405.10994/) (2024)
- [Private GANs, Revisited](https://mlsanity.com/paper/2302.02936/) (2023)
- [Global Convergence to the Equilibrium of GANs using Variational Inequalities](https://mlsanity.com/paper/1808.01531/) (2018)
- [How to DP-fy Your Data: A Practical Guide to Generating Synthetic Data With Differential Privacy](https://mlsanity.com/paper/2512.03238/) (2025)
- [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024)
- [Does Training with Synthetic Data Truly Protect Privacy?](https://mlsanity.com/paper/2502.12976/) (2025)
- [Output Perturbation for Differentially Private Convex Optimization: Faster and More General](https://mlsanity.com/paper/2102.04704/) (2021)
- [Function-space regularized R'enyi divergences](https://mlsanity.com/paper/2210.04974/) (2022)
- [A Pessimistic Approximation for the Fisher Information Measure](https://mlsanity.com/paper/1508.03878/) (2015)
- [Privacy Amplification Through Synthetic Data: Insights from Linear Regression](https://mlsanity.com/paper/2506.05101/) (2025)

## Abstract (arXiv)

We study privacy amplification by synthetic data release, a phenomenon in which differential privacy guarantees are improved by releasing only synthetic data rather than the private generative model itself. Recent work by Pierquin et al. (2025) established the first formal amplification guarantees for a linear generator, but they apply only in asymptotic regimes where the model dimension far exceeds the number of released synthetic records, limiting their practical relevance. In this work, we show a surprising result: under a bounded-parameter assumption, privacy amplification persists even when releasing an unbounded number of synthetic records, thereby improving upon the bounds of Pierquin et al. (2025). Our analysis provides structural insights that may guide the development of tighter privacy guarantees for more complex release mechanisms.