NeurIPS 2025

Private Evolution Converges
Tomas Gonzalez
Carnegie Mellon University
tcgonzal@andrew.cmu.edu
Giulia Fanti
Carnegie Mellon University
gfanti@andrew.cmu.edu
Aaditya Ramdas
Carnegie Mellon University
aramdas@cs.cmu.edu
Abstract
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 [33], PE produces an
(ε, δ)-DP synthetic dataset with expected 1-Wasserstein distance ˜O(d(nε)−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.
1
Introduction
Many modern machine learning applications rely on user data, making data privacy protection a
central concern. In this regard, differential privacy (DP) [17, 19] has become a de facto standard for
safeguarding sensitive information of individuals. Given a private dataset, many problems—including
regression [40, 12], deep learning [1], and stochastic optimization [6, 2]—can be performed in a DP
manner. While it is possible to design a different DP algorithm for each specific task, a reason...