# Stochastic Wasserstein Barycenters

arXiv: https://arxiv.org/abs/1802.05757 · HTML: https://mlsanity.com/paper/1802.05757/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 25 of 25)

- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023)
- [An Optimal Transport Approach to Personalized Federated Learning](https://mlsanity.com/paper/2206.02468/) (2022)
- [Fixed Support Tree-Sliced Wasserstein Barycenter](https://mlsanity.com/paper/2109.03431/) (2021)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [Measure Estimation in the Barycentric Coding Model](https://mlsanity.com/paper/2201.12195/) (2022)
- [Projection Robust Wasserstein Barycenters](https://mlsanity.com/paper/2102.03390/) (2021)
- [Variational Wasserstein Barycenters with c-Cyclical Monotonicity](https://mlsanity.com/paper/2110.11707/) (2021)
- [Nonparametric Teaching for Multiple Learners](https://mlsanity.com/paper/2311.10318/) (2023)
- [A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributions](https://mlsanity.com/paper/2405.03664/) (2024)
- [Learning to Generate Wasserstein Barycenters](https://mlsanity.com/paper/2102.12178/) (2021)
- [An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2203.00813/) (2022)
- [Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outliers](https://mlsanity.com/paper/2404.13401/) (2024)
- [Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentres](https://mlsanity.com/paper/2506.17197/) (2025)
- [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://mlsanity.com/paper/2509.24920/) (2025)
- [Differentially Private Wasserstein Barycenters](https://mlsanity.com/paper/2510.03021/) (2025)
- [Fixed-point iterations for several dissimilarity measure barycenters in the Gaussian case](https://mlsanity.com/paper/2205.04806/) (2022)
- [ScoreFusion: Fusing Score-based Generative Models via Kullback-Leibler Barycenters](https://mlsanity.com/paper/2406.19619/) (2024)
- [Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia](https://mlsanity.com/paper/2407.17329/) (2024)
- [Relax and Merge: A Simple Yet Effective Framework for Solving Fair k-Means and k-sparse Wasserstein Barycenter Problems](https://mlsanity.com/paper/2411.01115/) (2024)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)
- [An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem](https://mlsanity.com/paper/2304.11653/) (2023)
- [A Sub-4 Approximation for Fair k-Means](https://mlsanity.com/paper/2609.07974/) (2026)

## Abstract (arXiv)

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.