# On Differentially Private Sampling from Gaussian and Product Distributions

arXiv: https://arxiv.org/abs/2306.12549 · HTML: https://mlsanity.com/paper/2306.12549/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2023.

## Built on by (most cited first, 6 of 6)

- [Exactly Minimax-Optimal Locally Differentially Private Sampling](https://mlsanity.com/paper/2410.22699/) (2024)
- [Locally Private Sampling with Public Data](https://mlsanity.com/paper/2411.08791/) (2024)
- [Differentially Private Multi-Sampling from Distributions](https://mlsanity.com/paper/2412.10512/) (2024)
- [Locally Optimal Private Sampling: Beyond the Global Minimax](https://mlsanity.com/paper/2510.09485/) (2025)
- [Optimal Differentially Private Sampling of Unbounded Gaussians](https://mlsanity.com/paper/2503.01766/) (2025)
- [Reveal-or-Obscure: A Differentially Private Sampling Algorithm for Discrete Distributions](https://mlsanity.com/paper/2504.14696/) (2025)

## Abstract (arXiv)

Given a dataset of n i.i.d. samples from an unknown distribution P, we consider the problem of generating a sample from a distribution that is close to P in total variation distance, under the constraint of differential privacy (DP). We study the problem when P is a multi-dimensional Gaussian distribution, under different assumptions on the information available to the DP mechanism: known covariance, unknown bounded covariance, and unknown unbounded covariance. We present new DP sampling algorithms, and show that they achieve near-optimal sample complexity in the first two settings. Moreover, when P is a product distribution on the binary hypercube, we obtain a pure-DP algorithm whereas only an approximate-DP algorithm (with slightly worse sample complexity) was previously known.