mlsanityData to 7 Oct 2026

Wasserstein Iterative Networks for Barycenter Estimation

arXiv 2201.12245 ↗First posted 28 Jan 2022cs.LG stat.MLcited by 23

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Abstract (arXiv)

Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model. Previous approaches rely on regularization (entropic/quadratic) which introduces bias or on input convex neural networks which are not expressive enough for large-scale tasks. In contrast, our algorithm does not introduce bias and allows using arbitrary neural networks. In addition, based on the celebrity faces dataset, we construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms by using standard metrics of generative models such as FID.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 41 of its 75 references that are in the map. First posted on arXiv 28 Jan 2022.

Builds on

41 of 75 references.

References · 41

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29 more
  1. 2019Wasserstein-2 Generative Networkscited by 96
  2. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  3. 2021Generative Modeling with Optimal Transport Mapscited by 80
  4. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  5. 2021Representation Topology Divergence: A Method for Comparing Neural Network Representationscited by 66
  6. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
  7. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 49
  8. 2015Scalable Bayes via Barycenter in Wasserstein Spacecited by 44
  9. 2021Automatic Text Evaluation through the Lens of Wasserstein Barycenterscited by 38
  10. 2017Fruit recognition from images using deep learningcited by 35
  11. 20192-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANscited by 32
  12. 2020Continuous Regularized Wasserstein Barycenterscited by 32
  13. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  14. 2021Manifold Topology Divergence: a Framework for Comparing Data Manifoldscited by 31
  15. 2019On Scalable and Efficient Computation of Large Scale Optimal Transportcited by 29
  16. 2019Wasserstein Style Transfercited by 21
  17. 2017GAN and VAE from an Optimal Transport Point of Viewcited by 19
  18. 2019Progressive Wasserstein Barycenters of Persistence Diagramscited by 15
  19. 2020Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistencycited by 14
  20. 2019A gradual, semi-discrete approach to generative network training via explicit Wasserstein minimizationcited by 12
  21. 2019Barycenters of Natural Images -- Constrained Wasserstein Barycenters for Image Morphingcited by 11
  22. 2019Wasserstein Barycenter Model Ensemblingcited by 10
  23. 2018Data-driven regularization of Wasserstein barycenters with an application to multivariate density registrationcited by 8
  24. 2019Mixability of Integral Losses: a Key to Efficient Online Aggregation of Functional and Probabilistic Forecastscited by 7
  25. 2021Variational Wasserstein Barycenters with c-Cyclical Monotonicitycited by 7
  26. 2022On the Uniqueness of Kantorovich Potentialscited by 7
  27. 2021Learning to Generate Wasserstein Barycenterscited by 6
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  29. 2021Online learning with exponential weights in metric spacescited by 1

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Citing papers per year: 2022: 3; 2023: 8; 2024: 5; 2025: 7.

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  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  2. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  3. 2022Kernel Neural Optimal Transportcited by 31
  4. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  5. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  6. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  7. 2023Light Schr"odinger Bridgecited by 18
  8. 2023Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenterscited by 16
  9. 2025On the Relation between Rectified Flows and Optimal Transportcited by 15
  10. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  11. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  12. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
11 more
  1. 2024Improving Neural Optimal Transport via Displacement Interpolationcited by 7
  2. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  3. 2023Generating Synthetic Datasets by Interpolating along Generalized Geodesicscited by 5
  4. 2023Wasserstein Geodesic Generator for Conditional Distributionscited by 4
  5. 2023Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesicscited by 3
  6. 2024Relative Translation Invariant Wasserstein Distancecited by 3
  7. 2025Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimizationcited by 2
  8. 2025Meta Optimality for Demographic Parity Constrained Regression via Post-Processingcited by 2
  9. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  10. 2025Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computationcited by 1
  11. 2025Expert or not? assessing data quality in offline reinforcement learningcited by 1