mlsanityData to 7 Oct 2026

Learning to Generate Wasserstein Barycenters

arXiv 2102.12178 ↗First posted 24 Feb 2021cs.LG stat.MLcited by 6

Not on the map. Why?

Abstract (arXiv)

Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the problem of finding measures in-between given input measures in the optimal transport sense -- is even more computationally demanding as it requires to solve an optimization problem involving optimal transport distances. By training a deep convolutional neural network, we improve by a factor of 60 the computational speed of Wasserstein barycenters over the fastest state-of-the-art approach on the GPU, resulting in milliseconds computational times on 512×512 regular grids. We show that our network, trained on Wasserstein barycenters of pairs of measures, generalizes well to the problem of finding Wasserstein barycenters of more than two measures. We demonstrate the efficiency of our approach for computing barycenters of sketches and transferring colors between multiple images.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 35 of its 67 references that are in the map. First posted on arXiv 24 Feb 2021.

Builds on

35 of 67 references.

References · 35

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23 more
  1. 2016Input Convex Neural Networkscited by 407
  2. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  3. 2013Fast Computation of Wasserstein Barycenterscited by 216
  4. 2015Learning with a Wasserstein Losscited by 194
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  16. 2018Stochastic Wasserstein Barycenterscited by 25
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  18. 2019Ground Metric Learning on Graphscited by 17
  19. 2015Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metriccited by 15
  20. 2019Learning Embeddings into Entropic Wasserstein Spacescited by 15
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  22. 2018Variational Wasserstein Clusteringcited by 11
  23. 2019Wasserstein Barycenter Model Ensemblingcited by 10

Built on by

Cited by year

Citing papers per year: 2022: 3; 2023: 2; 2024: 1.

6 papers.

  1. 2022Meta Optimal Transportcited by 28
  2. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  3. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  4. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  5. 2022GeONet: a neural operator for learning the Wasserstein geodesiccited by 3
  6. 2023Beckman Defensecited by 0