# Private Wasserstein Distance

arXiv: https://arxiv.org/abs/2404.06787 · HTML: https://mlsanity.com/paper/2404.06787/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [Multimodal Misinformation Detection by Learning from Synthetic Data with Multimodal LLMs](https://mlsanity.com/paper/2409.19656/) (2024)
- [Consistent Estimation of Numerical Distributions under Local Differential Privacy by Wavelet Expansion](https://mlsanity.com/paper/2509.19661/) (2025)
- [When Sample Selection Bias Precipitates Model Collapse](https://mlsanity.com/paper/2606.13732/) (2026)
- [Illuminant and light direction estimation using Wasserstein distance method](https://mlsanity.com/paper/2503.05802/) (2025)

## Abstract (arXiv)

Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant challenges. Existing approaches, such as Differential Privacy and Federated Optimization, have been employed to estimate the Wasserstein distance under such constraints. However, these methods often fall short when both accuracy and security are required. In this study, we explore the inherent triangular properties within the Wasserstein space, leading to a novel solution named TriangleWad. This approach facilitates the fast computation of the Wasserstein distance between datasets stored across different entities, ensuring that raw data remain completely hidden. TriangleWad not only strengthens resistance to potential attacks but also preserves high estimation accuracy. Through extensive experiments across various tasks involving both image and text data, we demonstrate its superior performance and significant potential for real-world applications.