Research map / Learning theory and algorithms / Optimal transport
Transport map estimation
Estimate and regularize transport maps with statistical and low-rank guarantees.
77 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimal transport, keyword cluster “optimal transport · transport ot · sinkhorn”
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.
29 papers in 2023–24 and 22 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 34.5% to 15.5%.
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 · Mapping Estimation for Discrete Optimal Transport (NeurIPS 2016 · 60 citations)
- 2019 · Hierarchical Optimal Transport for Multimodal Distribution Alignment (NeurIPS 2019 · 30 citations)
- 2020 · Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form (NeurIPS 2020 · 41 citations)
- 2021 · Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections (NeurIPS 2021 · 27 citations)
- 2022 · Supervised Training of Conditional Monge Maps (NeurIPS 2022 · 13 citations)
- 2023 · Sliced Optimal Partial Transport (CVPR 2023 · 8 citations)
- 2024 · Double-Bounded Optimal Transport for Advanced Clustering and Classification (AAAI 2024 · 5 citations)
- 2025 · Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan (ICML 2025 · 0 citations)
- 2026 · Variational Entropic Optimal Transport (ICML 2026 · 0 citations)
Earliest papers here
- Mapping Estimation for Discrete Optimal Transport (NeurIPS 2016 · 60 citations)
- Hierarchical Optimal Transport for Multimodal Distribution Alignment (NeurIPS 2019 · 30 citations)
- A Graph Theoretic Additive Approximation of Optimal Transport (NeurIPS 2019 · 12 citations)
What has been tried
59 papers here report 481 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 19%, 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 |
|---|---|---|---|---|
| add barycenter reweighting | Gaussian mixture synthetic clustering · Top-1 accuracy | 88.00% -> 100.00% | Helped | Double-Bounded Optimal Transport for Advanced Clustering and Classification (AAAI 2024 · 5 citations) |
| add latent noise z to the class-guided transport map | FMNIST → MNIST · accuracy | 82.79 -> 83.22 | Helped | Neural Optimal Transport with General Cost Functionals (ICLR 2024 · 3 citations) |
| recompute MST projections throughout training rather than skipping them until the final iteration | Noisy random tree, σ=5 · Wasserstein error | 0.279 ± 0.102 -> 0.262 ± 0.102 | Helped | Learning Ultrametric Trees for Optimal Transport Regression (AAAI 2024 · 2 citations) |
| Replace the uniform cubic partition with a non-uniform partition | Distributions where μ has bounded 2p-th moments · expected transportation error (E_p) | \widetilde{O} (p,d)\bigl(n^{-1/(d+2p)}\bigr) | Helped | Estimation of Stochastic Optimal Transport Maps (NeurIPS 2025 · 0 citations) |
| Use Beta (2,2) time sampling instead of uniform | Wild→Cat (64x64) · FID | 10.72 -> 12.46 | Hurt | Improving Neural Optimal Transport via Displacement Interpolation (ICLR 2025 · 0 citations) |
| Increase temperature parameter τ | Point Cloud MNIST 2D interpolation · mass splitting | Helped | Expected Sliced Transport Plans (ICLR 2025 · 0 citations) | |
| Use GST-Φ1 instead of GST-Φ0 | TWITTER, RECIPE, CLASSIC, AMAZON · classification performance | Helped | Generalized Sobolev Transport for Probability Measures on a Graph (ICML 2024 · 0 citations) | |
| optimize marginal distributions with L_M rather than transport plans with L_T | Synthetic linear perturbation, L2 cost · L2 | 0.45 -> 0.41 | Helped | Quantum Theory and Application of Contextual Optimal Transport (ICML 2024 · 0 citations) |
| use ε-KL cost functions instead of classical cost functions | Ave, celeba! manifold k=1, k=2, and k=3 · FID | 30.7 -> 34.5; 31.0 -> 34.9; 31.7 -> 35.7 | Hurt | Estimating Barycenters of Distributions with Neural Optimal Transport (ICML 2024 · 0 citations) |
| increase expectile τ from 0.5 to 0.9 | Synthetic 2D · W2 | 33.47 -> 0.06 | Helped | Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport (NeurIPS 2024 · 0 citations) |
| Vary the step-length schedule (accelerated, constant-speed, or decelerated) | Synthetic data and sci-Plex · Sinkhorn divergence | No clear effect | Progressive Entropic Optimal Transport Solvers (NeurIPS 2024 · 0 citations) | |
| Increase the share of displacement inertia captured by the p* subspace | Synthetic ground-truth subspace recovery · Normalized squared-residual error | Helped | Learning Elastic Costs to Shape Monge Displacements (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 14 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 5 of 14 papers
- CIFAR-10 · 2 of 14 papers
Baselines
- OTM · 2 of 14 papers
- DSBM · 2 of 14 papers
- ASBM · 2 of 14 papers
- Sinkhorn · 2 of 14 papers
- ProgOT · 2 of 14 papers
- LOT · 2 of 14 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 51 papers; from OpenAlex and the papers' affiliations).
- Skolkovo Institute of Science and Technology · 8 papers
- Ensae ParisTech · 5 papers
- Apple · 4 papers
- New York University · 3 papers
- Dalian University of Technology · 2 papers
- Google · 2 papers
- ITMO University · 2 papers
- Vanderbilt University · 2 papers
- Microsoft · 2 papers
- ETHZ - ETH Zurich · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Neural optimal transport (99 papers)
- Sinkhorn and entropic OT algorithms (69 papers)
- Schrodinger bridge matching (11 papers)
Elsewhere in the topic
- Wasserstein barycenters and GW (55 papers)
- Sliced Wasserstein variants (50 papers)
- Wasserstein losses for generative models (23 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).