# Private Evolution Converges

arXiv: https://arxiv.org/abs/2506.08312 · HTML: https://mlsanity.com/paper/2506.08312/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 10 Jun 2025.

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

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Differentially Private Diffusion Models](https://mlsanity.com/paper/2210.09929/) (2022)
- [Differentially Private Synthetic Data via Foundation Model APIs 2: Text](https://mlsanity.com/paper/2403.01749/) (2024)
- [Differentially Private Synthetic Data via Foundation Model APIs 1: Images](https://mlsanity.com/paper/2305.15560/) (2023)
- [Don't Generate Me: Training Differentially Private Generative Models with Sinkhorn Divergence](https://mlsanity.com/paper/2111.01177/) (2021)
- [G-PATE: Scalable Differentially Private Data Generator via Private Aggregation of Teacher Discriminators](https://mlsanity.com/paper/1906.09338/) (2019)
- [Differentially Private Query Release Through Adaptive Projection](https://mlsanity.com/paper/2103.06641/) (2021)
- [Differentially Private Stochastic Optimization: New Results in Convex and Non-Convex Settings](https://mlsanity.com/paper/2107.05585/) (2021)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [Faster Rates of Convergence to Stationary Points in Differentially Private Optimization](https://mlsanity.com/paper/2206.00846/) (2022)
- [PrE-Text: Training Language Models on Private Federated Data in the Age of LLMs](https://mlsanity.com/paper/2406.02958/) (2024)
- [Differentially Private Sliced Wasserstein Distance](https://mlsanity.com/paper/2107.01848/) (2021)
- [Generating Private Synthetic Data with Genetic Algorithms](https://mlsanity.com/paper/2306.03257/) (2023)
- [Efficient Algorithms for Privately Releasing Marginals via Convex Relaxations](https://mlsanity.com/paper/1308.1385/) (2013)
- [Adaptive Metric Dimensionality Reduction](https://mlsanity.com/paper/1302.2752/) (2013)
- [Benchmarking Differentially Private Tabular Data Synthesis](https://mlsanity.com/paper/2504.14061/) (2025)
- [POPri: Private Federated Learning using Preference-Optimized Synthetic Data](https://mlsanity.com/paper/2504.16438/) (2025)
- [Differentially Private Synthetic Data via APIs 3: Using Simulators Instead of Foundation Model](https://mlsanity.com/paper/2502.05505/) (2025)
- [Algorithmically Effective Differentially Private Synthetic Data](https://mlsanity.com/paper/2302.05552/) (2023)
- [Contrastive Private Data Synthesis via Weighted Multi-PLM Fusion](https://mlsanity.com/paper/2502.00245/) (2025)
- [DPImageBench: A Unified Benchmark for Differentially Private Image Synthesis](https://mlsanity.com/paper/2503.14681/) (2025)
- [Differentially Private Normalizing Flows for Privacy-Preserving Density Estimation](https://mlsanity.com/paper/2103.14068/) (2021)
- [Certified private data release for sparse Lipschitz functions](https://mlsanity.com/paper/2302.09680/) (2023)
- [Is API Access to LLMs Useful for Generating Private Synthetic Tabular Data?](https://mlsanity.com/paper/2502.06555/) (2025)
- [Differentially Private Gradient Flow based on the Sliced Wasserstein Distance](https://mlsanity.com/paper/2312.08227/) (2023)
- [Online Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2402.08012/) (2024)

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

- [Minimax optimal differentially private synthetic data for smooth queries](https://mlsanity.com/paper/2602.01607/) (2026)
- [ContinuousBench: Can Differentially Private Synthetic Text Improve Capabilities?](https://mlsanity.com/paper/2606.01849/) (2026)

## Abstract (arXiv)

Private Evolution (PE) is a promising training-free method for differentially private (DP) synthetic data generation. While it achieves strong performance in some domains (e.g., images and text), its behavior in others (e.g., tabular data) is less consistent. To date, the only theoretical analysis of the convergence of PE depends on unrealistic assumptions about both the algorithm's behavior and the structure of the sensitive dataset. In this work, we develop a new theoretical framework to understand PE's practical behavior and identify sufficient conditions for its convergence. For d-dimensional sensitive datasets with n data points from a convex and compact domain, we prove that under the right hyperparameter settings and given access to the Gaussian variation API proposed in citePE23, PE produces an (varepsilon, δ)-DP synthetic dataset with expected 1-Wasserstein distance tildeO(d(nvarepsilon)-1/d) from the original; this establishes worst-case convergence of the algorithm as n → ∞. Our analysis extends to general Banach spaces as well. We also connect PE to the Private Signed Measure Mechanism, a method for DP synthetic data generation that has thus far not seen much practical adoption. We demonstrate the practical relevance of our theoretical findings in experiments.