# Statistical optimal transport

arXiv: https://arxiv.org/abs/2407.18163 · HTML: https://mlsanity.com/paper/2407.18163/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 325 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Built on by (most cited first, 30 of 47)

- [Controlling Language and Diffusion Models by Transporting Activations](https://mlsanity.com/paper/2410.23054/) (2024)
- [Quantitative Clustering in Mean-Field Transformer Models](https://mlsanity.com/paper/2504.14697/) (2025)
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- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [On Fitting Flow Models with Large Sinkhorn Couplings](https://mlsanity.com/paper/2506.05526/) (2025)
- [Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models](https://mlsanity.com/paper/2506.13061/) (2025)
- [Plug-in estimation of Schr"odinger bridges](https://mlsanity.com/paper/2408.11686/) (2024)
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- [DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows](https://mlsanity.com/paper/2503.01140/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Federate the Router: Learning Language Model Routers with Sparse and Decentralized Evaluations](https://mlsanity.com/paper/2601.22318/) (2026)
- [Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions](https://mlsanity.com/paper/2605.30153/) (2026)
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- [Optimal Robust Estimation under Local and Global Corruptions: Stronger Adversary and Smaller Error](https://mlsanity.com/paper/2410.17230/) (2024)
- [Manifold learning in metric spaces](https://mlsanity.com/paper/2503.16187/) (2025)
- [Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space](https://mlsanity.com/paper/2507.01709/) (2025)
- [Gradient Flow Sampler-based Distributionally Robust Optimization](https://mlsanity.com/paper/2510.25956/) (2025)
- [On The Hidden Biases of Flow Matching Samplers](https://mlsanity.com/paper/2512.16768/) (2025)
- [Convergence Rates for Distribution Matching with Sliced Optimal Transport](https://mlsanity.com/paper/2602.10691/) (2026)
- [A Unifying View of Variational Generative Wasserstein Flows](https://mlsanity.com/paper/2605.31369/) (2026)
- [Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applications](https://mlsanity.com/paper/2410.23602/) (2024)
- [Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives](https://mlsanity.com/paper/2506.19025/) (2025)
- [Measuring Time-Series Dataset Similarity using Wasserstein Distance](https://mlsanity.com/paper/2507.22189/) (2025)
- [Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation](https://mlsanity.com/paper/2510.04602/) (2025)
- [Particle Dynamics for Latent-Variable Energy-Based Models](https://mlsanity.com/paper/2510.15447/) (2025)

## Abstract (arXiv)

We present an introduction to the field of statistical optimal transport, based on lectures given at 'Ecole d''Et'e de Probabilit'es de Saint-Flour XLIX.