Research map / Learning theory and algorithms / Optimal transport
Sliced Wasserstein variants
Develop sliced and tree-sliced Wasserstein distances with faster approximations and kernels.
50 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimal transport, keyword cluster “wasserstein distance · sliced · sw”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
7 papers in 2023–24 and 26 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 8.3% to 18.3%.
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 · Sliced Wasserstein Kernels for Probability Distributions (CVPR 2016 · 144 citations)
- 2017 · Sliced Wasserstein Kernel for Persistence Diagrams (ICML 2017 · 151 citations)
- 2018 · Learning Wasserstein Embeddings (ICLR 2018 · 8 citations)
- 2019 · Sliced Gromov-Wasserstein (NeurIPS 2019 · 23 citations)
- 2020 · Scalable Nearest Neighbor Search for Optimal Transport (ICML 2020 · 10 citations)
- 2021 · Distributional Sliced-Wasserstein and Applications to Generative Modeling (ICLR 2021 · 9 citations)
- 2022 · Distributional Convergence of the Sliced Wasserstein Process (NeurIPS 2022 · 5 citations)
- 2023 · Near-Linear Time Algorithm for the Chamfer Distance (NeurIPS 2023 · 7 citations)
- 2024 · Stereographic Spherical Sliced Wasserstein Distances (ICML 2024 · 0 citations)
- 2025 · Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances (ICML 2025 · 0 citations)
- 2026 · A Novel Sliced Fused Gromov-Wasserstein Distance (AAAI 2026 · 1 citation)
Earliest papers here
- Sliced Wasserstein Kernels for Probability Distributions (CVPR 2016 · 144 citations)
- Flattening the Density Gradient for Eliminating Spatial Centrality to Reduce Hubness (AAAI 2016 · 9 citations)
- Sliced Wasserstein Kernel for Persistence Diagrams (ICML 2017 · 151 citations)
What has been tried
38 papers here report 329 measured changes (a component added, removed or swapped, compared with a baseline): helped 72%, no clear effect 7%, hurt 16%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Set the CircularTSW radius to r=0 | 25 Gaussians, iteration 2500 · W₂ distance | 7.86e-3 -> 8.94e-3 | Hurt | Tree-Sliced Wasserstein Distance with Nonlinear Projection (ICML 2025 · 0 citations) |
| Increase the number of s-OTDD projections | MNIST and CIFAR10 distance correlation with OTDD (Exact) · correlation | Helped | Lightspeed Geometric Dataset Distance via Sliced Optimal Transport (ICML 2025 · 0 citations) | |
| use a neural-network projector instead of a linear projector | CIFAR-10, Euler · FID | 4.16 ± 0.09 -> \textbf{3.62} ± 0.05 | Helped | Differentiable Generalized Sliced Wasserstein Plans (NeurIPS 2025 · 0 citations) |
| Use 3-child trees instead of 2-child trees | Synthetic torus dataset · Frobenius norm error | Helped | Fast unsupervised ground metric learning with tree-Wasserstein distance (ICLR 2025 · 0 citations) | |
| use orthogonal directions instead of unrestricted directions | CIFAR-10 · FID | 2.60 -> 2.525 | Helped | Distance-Based Tree-Sliced Wasserstein Distance (ICLR 2025 · 0 citations) |
| increase UltraTree training-distribution sparsity from 1% to 2% | Reuters and Ohsumed · RE-W | Reuters: 0.041±0.003 -> 0.061±0.002; Ohsumed: 0.038±0.001 -> 0.069±0.001 | Hurt | UltraTWD: Optimizing Ultrametric Trees for Tree-Wasserstein Distance (ICML 2025) |
| Use ETD A4 instead of basic ETD A1 | Outex · accuracy | 0.89 -> 0.99 | Helped | A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams (AAAI 2024) |
What reviewers will expect
Datasets and baselines named in the 18 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- CIFAR-10 · 7 of 18 papers
- MNIST · 3 of 18 papers
- Swiss Roll · 3 of 18 papers
- 25 Gaussians · 2 of 18 papers
- AG News · 2 of 18 papers
Baselines
- SW · 4 of 18 papers
- MaxSW · 3 of 18 papers
- SWGG · 3 of 18 papers
- LCVSW · 3 of 18 papers
- SSW · 3 of 18 papers
- S3W · 3 of 18 papers
- Sinkhorn divergence · 2 of 18 papers
- DSW · 2 of 18 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 33 papers; from OpenAlex and the papers' affiliations).
- National University of Singapore · 4 papers
- University of Texas, Austin · 3 papers
- Google · 3 papers
- VinAI Research · 3 papers
- The Institute of Statistical Mathematics · 3 papers
- University of Texas at Austin · 2 papers
- Massachusetts Institute of Technology · 2 papers
- VinUniversity · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Wasserstein barycenters and GW (55 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).