Wasserstein Barycenters

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Wasserstein barycenters summarize several probability distributions by finding a distribution that minimizes their weighted transport cost, preserving geometry that ordinary averaging can erase. They support tasks such as distribution alignment, multimodal fusion, robust aggregation, and summarizing spatial or graph data. Methods range from discrete optimization and entropic regularization to sliced transport, Bures-Wasserstein matrix methods, and gradient- or flow-based procedures for generating barycenter samples. A central challenge is balancing geometric fidelity and theoretical guarantees with computational cost, particularly in high dimensions or with heterogeneous data, while extending methods beyond a single fixed barycenter.

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11 papers2 papers in the last four weeks, down 50% on the four weeks before. 0.0% of all new papers.

Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data
Oct 21, 2026Ngoc-Hai Nguyen, Thuan Nguyen, Prakash Ishwar +1Wasserstein Barycenters Schrödinger Bridges
Department of Electrical and Computer Engineering Tufts University · Department of Engineering, Engineering Technology East Tennessee State University · Department of Electrical and Computer Engineering Boston University +1
Towards Universal Wasserstein Barycenters through Flow Matching
Sep 29, 2026Eduardo Fernandes MontesumaWasserstein Barycenters Optimal Transport
Sigma Nova Paris, France
Binding Multiple Modalities via Multimodal Wasserstein Barycenter
Sep 27, 2026Xiaole Tang, Jiayi Xu, Xiang Gu +2Cross-Modal Alignment Multimodal Embedding
Xi’an Jiaotong University
SWB-DM: A Calibrated Sliced-Wasserstein-Barycenter Aggregator with Delayed-Momentum Caching for Byzantine-Robust Federated Learning under Partial Participation
Sep 14, 2026Saranraj S, Saranya M S, Alex David S +1Federated Learning Aggregation Byzantine-Robust Federated Learning
Department of AIML Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai, India · Assistant Professor, Department of AIML Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai, India · Professor, Department of AIML Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai, India
A Tight 3-Approximation for Fair $k$ -Means
Sep 7, 2026Kangke Cheng, Guanlin Mo, Shihong Song +1Clustering Group Fairness
University of Science and Technology of China, Hefei, China · School of Informatics, University of Edinburgh, Edinburgh, UK
Projected Riemannian Gradient Descent for the Bures-Wasserstein Barycenter: Dimension-Independent Linear Convergence at Unit Step Size
Sep 3, 2026A. AfhamRiemannian Optimization Optimization Convergence Analysis
Centre for Quantum Technologies, National University of Singapore, Singapore
Multi-Source Wasserstein Distributionally Robust Graph Learning
Aug 20, 2026Chuansen Peng, Yifan Xia, Jinshan Zhong +1Graph Structure Learning Graph Representation Learning
School of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China · School of Statistics and Data Science, Southwestern University of Finance and Economics, Chengdu, Sichuan, 611130, China
Wasserstein Policy Learning for Distributional Outcomes
Jun 17, 2026Yiyan Huang, Cheuk Hang Leung, Qi Wu +1Offline RL Wasserstein Barycenters
School of Statistics and Data Science & Institute of Big Data Research, Shanghai University of Finance and Economics, Shanghai, China
DeFed-GMM-DaDiL: A Decentralized Federated Framework for Domain Adaptation
May 5, 2026Rebecca Clain, Eduardo Fernandes Montesuma, Fred Ngole MboulaMulti-Source Domain Adaptation Domain Adaptation
Universit´e Paris-Saclay, CEA, List, F-91120 Palaiseau, France · Sigma Nova
Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting
Apr 24, 2026Younes Essafouri, Laure Raynaud, Luciano Drozda +1Gradient-Based Attribution Neural Network Interpretability
Univ. Toulouse, INSA Toulouse, CNRS UMR 5219, IMT, Toulouse, France · Météo-France, CNRS, Univ. Toulouse, CNRM, Toulouse, France · Cerfacs, CNRS/Cerfacs/IRD, CECI, Toulouse, France
Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs
Mar 27, 2026David Gentile, James M. MurphyWasserstein Barycenters Optimal Transport
Tufts University, Dept. of Mathematics, Medford, MA, USA

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Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data

Ngoc-Hai Nguyen, Thuan Nguyen, Prakash Ishwar, Shuchin Aeron

Department of Electrical and Computer Engineering Tufts University · Department of Engineering, Engineering Technology East Tennessee State University · Department of Electrical and Computer Engineering Boston University+1

Wasserstein Barycenters Schrödinger Bridges

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Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual drift-diffusion control arising in the recently proposed Schrödinger-Bass Bridge (SBB) between two measures, and propose SBB-encoder, SBB-decoder, SBB-symmetric, and SBB-Markovian barycenter models. For each of these novel models, our first theoretical result establishes the existence of the SBB-barycenter under mild assumptions. Our second theoretical result characterizes the decoder SBB-barycenter of Gaussians where we show that for Gaussian input measures, the decoder formulation admits a Gaussian minimizer, reducing barycenter computation to a finite-dimensional optimization and yielding a compact algorithm. For general input measures, we derive a hybrid Wasserstein gradient particle descent scheme for all four formulations using the SBB dual representation. Finally, we utilize these algorithms for solving distributional-inverse/interpolation problems arising in the context of spatial images and single-cell RNA sequencing data, where we show that the SBB-decoder and Markovian barycenter allow us to interpolate between successive time points. Results show that our method outperforms existing barycenter models for measure interpolation and inference.