# Recent Advances in Optimal Transport for Machine Learning

arXiv: https://arxiv.org/abs/2306.16156 · HTML: https://mlsanity.com/paper/2306.16156/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Builds on 86 of its 202 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 30 of 86)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)

## Built on by (most cited first, 30 of 66)

- [TopV: Compatible Token Pruning with Inference Time Optimization for Fast and Low-Memory Multimodal Vision Language Model](https://mlsanity.com/paper/2503.18278/) (2025)
- [The Evolution of Dataset Distillation: Toward Scalable and Generalizable Solutions](https://mlsanity.com/paper/2502.05673/) (2025)
- [Beyond FVD: Enhanced Evaluation Metrics for Video Generation Quality](https://mlsanity.com/paper/2410.05203/) (2024)
- [LanDA: Language-Guided Multi-Source Domain Adaptation](https://mlsanity.com/paper/2401.14148/) (2024)
- [Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space](https://mlsanity.com/paper/2307.14953/) (2023)
- [Differentiable Generalized Sliced Wasserstein Plans](https://mlsanity.com/paper/2505.22049/) (2025)
- [The Synergy Between Optimal Transport Theory and Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2401.10949/) (2024)
- [ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport](https://mlsanity.com/paper/2403.03777/) (2024)
- [Score-Based Diffusion Policy Compatible with Reinforcement Learning via Optimal Transport](https://mlsanity.com/paper/2502.12631/) (2025)
- [Your contrastive learning problem is secretly a distribution alignment problem](https://mlsanity.com/paper/2502.20141/) (2025)
- [Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport](https://mlsanity.com/paper/2404.10261/) (2024)
- [PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport](https://mlsanity.com/paper/2502.03749/) (2025)
- [Benchmarking Domain Adaptation for Chemical Processes on the Tennessee Eastman Process](https://mlsanity.com/paper/2308.11247/) (2023)
- [Federated Dataset Dictionary Learning for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2309.07670/) (2023)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [Dude: Dual Distribution-Aware Context Prompt Learning For Large Vision-Language Model](https://mlsanity.com/paper/2407.04489/) (2024)
- [Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport](https://mlsanity.com/paper/2502.12793/) (2025)
- [Towards Reasoning-Preserving Unlearning in Multimodal Large Language Models](https://mlsanity.com/paper/2512.17911/) (2025)
- [Optimal Transport for Domain Adaptation through Gaussian Mixture Models](https://mlsanity.com/paper/2403.13847/) (2024)
- [A dimensionality reduction technique based on the Gromov-Wasserstein distance](https://mlsanity.com/paper/2501.13732/) (2025)
- [Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysis](https://mlsanity.com/paper/2510.11829/) (2025)
- [DMGD: Train-Free Dataset Distillation with Semantic-Distribution Matching in Diffusion Models](https://mlsanity.com/paper/2605.03877/) (2026)
- [Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena](https://mlsanity.com/paper/2505.06123/) (2025)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport](https://mlsanity.com/paper/2604.02610/) (2026)
- [GSINA: Improving Subgraph Extraction for Graph Invariant Learning via Graph Sinkhorn Attention](https://mlsanity.com/paper/2402.07191/) (2024)
- [Dataset Dictionary Learning in a Wasserstein Space for Federated Domain Adaptation](https://mlsanity.com/paper/2407.11647/) (2024)
- [Learning signals defined on graphs with optimal transport and Gaussian process regression](https://mlsanity.com/paper/2410.15721/) (2024)
- [Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterin](https://mlsanity.com/paper/2501.18143/) (2025)

## Abstract (arXiv)

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to different problems in machine learning, such as generative modeling and transfer learning. In this survey we explore contributions of Optimal Transport for Machine Learning over the period 2012 -- 2023, focusing on four sub-fields of Machine Learning: supervised, unsupervised, transfer and reinforcement learning. We further highlight the recent development in computational Optimal Transport and its extensions, such as partial, unbalanced, Gromov and Neural Optimal Transport, and its interplay with Machine Learning practice.