Research map / Learning theory and algorithms / Optimal transport
Wasserstein barycenters and GW
Compute Wasserstein barycenters, projection-robust and Gromov-Wasserstein distances with new optimization methods.
55 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimal transport, keyword cluster “wasserstein distance · sliced · sw”
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Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
8 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 9.5% to 10.6%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Gromov-Wasserstein Averaging of Kernel and Distance Matrices (ICML 2016 · 216 citations)
- 2017 · Order-Preserving Wasserstein Distance for Sequence Matching (CVPR 2017 · 56 citations)
- 2018 · Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance (NeurIPS 2018 · 70 citations)
- 2019 · Subspace Robust Wasserstein Distances (ICML 2019 · 50 citations)
- 2020 · Synchronizing Probability Measures on Rotations via Optimal Transport (CVPR 2020 · 34 citations)
- 2021 · The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation (NeurIPS 2021 · 40 citations)
- 2022 · Computing Wasserstein-p Distance Between Images With Linear Cost (CVPR 2022 · 7 citations)
- 2023 · A Riemannian Exponential Augmented Lagrangian Method for Computing the Projection Robust Wasserstein Distance (NeurIPS 2023 · 1 citation)
- 2024 · A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributions (ICML 2024 · 3 citations)
- 2025 · Linear Partial Gromov-Wasserstein Embedding (ICLR 2025 · 0 citations)
- 2026 · Gromov-Wasserstein at Scale, Beyond Squared Norms (ICML 2026 · 0 citations)
Earliest papers here
- Gromov-Wasserstein Averaging of Kernel and Distance Matrices (ICML 2016 · 216 citations)
- Order-Preserving Wasserstein Distance for Sequence Matching (CVPR 2017 · 56 citations)
- S2JSD-LSH: A Locality-Sensitive Hashing Schema for Probability Distributions (AAAI 2017 · 10 citations)
What has been tried
40 papers here report 310 measured changes (a component added, removed or swapped, compared with a baseline): helped 70%, no clear effect 6%, hurt 17%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add momentum to the MMD flow | MNIST and CIFAR10 · convergence speed | Helped | Generative Sliced MMD Flows with Riesz Kernels (ICLR 2024 · 1 citation) |
Recent preprints
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Related approaches
Same keyword cluster
- Sliced Wasserstein variants (50 papers)
- Wasserstein losses for generative models (23 papers)
Elsewhere in the topic
- Neural optimal transport (99 papers)
- Transport map estimation (77 papers)
- Sinkhorn and entropic OT algorithms (69 papers)
- Schrodinger bridge matching (11 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).