# Differentially Private Sampling from Distributions via Wasserstein Projection

arXiv: https://arxiv.org/abs/2605.10015 · HTML: https://mlsanity.com/paper/2605.10015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 13 of 13)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Learning with User-Level Privacy](https://mlsanity.com/paper/2102.11845/) (2021)
- [Optimal Algorithms for Mean Estimation under Local Differential Privacy](https://mlsanity.com/paper/2205.02466/) (2022)
- [Differentially Private Sliced Wasserstein Distance](https://mlsanity.com/paper/2107.01848/) (2021)
- [InvisibleInk: High-Utility and Low-Cost Text Generation with Differential Privacy](https://mlsanity.com/paper/2507.02974/) (2025)
- [Instance-Optimal Private Density Estimation in the Wasserstein Distance](https://mlsanity.com/paper/2406.19566/) (2024)
- [Constructing elastic distinguishability metrics for location privacy](https://mlsanity.com/paper/1503.00756/) (2015)
- [Exactly Minimax-Optimal Locally Differentially Private Sampling](https://mlsanity.com/paper/2410.22699/) (2024)
- [Learning with Differentially Private (Sliced) Wasserstein Gradients](https://mlsanity.com/paper/2502.01701/) (2025)
- [Differentially Private Wasserstein Barycenters](https://mlsanity.com/paper/2510.03021/) (2025)
- [Locally Optimal Private Sampling: Beyond the Global Minimax](https://mlsanity.com/paper/2510.09485/) (2025)

## Abstract (arXiv)

In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such formulations suffer from two key limitations: 1) they fail to capture the geometric structure of the support, and 2) they are not applicable when the supports of the distributions differ. To deal with these issues, we develop a novel framework for DP sampling with Wasserstein distance as the utility measure. In this formulation, we propose Wasserstein Projection Mechanism (WPM), a minimax optimal mechanism based on Wasserstein projection. Furthermore, we develop efficient algorithms for computing the proposed mechanisms approximately and provide convergence guarantees.