# Orthogonal Estimation of Wasserstein Distances

arXiv: https://arxiv.org/abs/1903.03784 · HTML: https://mlsanity.com/paper/1903.03784/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2019.

## Built on by (most cited first, 30 of 32)

- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [On the Expressive Power of Self-Attention Matrices](https://mlsanity.com/paper/2106.03764/) (2021)
- [Energy-Based Sliced Wasserstein Distance](https://mlsanity.com/paper/2304.13586/) (2023)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Wasserstein Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.07940/) (2021)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Expected Sliced Transport Plans](https://mlsanity.com/paper/2410.12176/) (2024)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Scalable Infomin Learning](https://mlsanity.com/paper/2302.10701/) (2023)
- [Image Generation with a Sphere Encoder](https://mlsanity.com/paper/2602.15030/) (2026)
- [A User's Guide to Sampling Strategies for Sliced Optimal Transport](https://mlsanity.com/paper/2502.02275/) (2025)
- [Repelling Random Walks](https://mlsanity.com/paper/2310.04854/) (2023)
- [Sliced Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2102.07115/) (2021)
- [Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics](https://mlsanity.com/paper/2307.01770/) (2023)
- [Task Adaptation from Skills: Information Geometry, Disentanglement, and New Objectives for Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2506.10629/) (2025)
- [Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances](https://mlsanity.com/paper/2509.20508/) (2025)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations](https://mlsanity.com/paper/2401.11354/) (2024)
- [Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis](https://mlsanity.com/paper/2502.06525/) (2025)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [Sliced-Regularized Optimal Transport](https://mlsanity.com/paper/2604.23944/) (2026)
- [Heterogeneous Wasserstein Discrepancy for Incomparable Distributions](https://mlsanity.com/paper/2106.02542/) (2021)
- [A Simple Way to Learn Metrics Between Attributed Graphs](https://mlsanity.com/paper/2209.12727/) (2022)
- [Keep your distance: learning dispersed embeddings on mathbbSm](https://mlsanity.com/paper/2502.08231/) (2025)
- [Repulsive Monte Carlo on the sphere for the sliced Wasserstein distance](https://mlsanity.com/paper/2509.10166/) (2025)
- [Wasserstein Diversity-Enriched Regularizer for Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2308.00989/) (2023)
- [Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein](https://mlsanity.com/paper/2605.13753/) (2026)

## Abstract (arXiv)

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.