# Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey

arXiv: https://arxiv.org/abs/2305.05080 · HTML: https://mlsanity.com/paper/2305.05080/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 200 of its 317 references that are in the map.
- First posted on arXiv 8 May 2023.

## Builds on (most cited first, 30 of 200)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [AttGAN: Facial Attribute Editing by Only Changing What You Want](https://mlsanity.com/paper/1711.10678/) (2017)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)

## Built on by (most cited first, 27 of 27)

- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [AWT: Transferring Vision-Language Models via Augmentation, Weighting, and Transportation](https://mlsanity.com/paper/2407.04603/) (2024)
- [Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmark](https://mlsanity.com/paper/2306.10161/) (2023)
- [Joint Self-Supervised Video Alignment and Action Segmentation](https://mlsanity.com/paper/2503.16832/) (2025)
- [OTSurv: A Novel Multiple Instance Learning Framework for Survival Prediction with Heterogeneity-aware Optimal Transport](https://mlsanity.com/paper/2506.20741/) (2025)
- [ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport](https://mlsanity.com/paper/2403.03777/) (2024)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)
- [Domain-aware Category-level Geometry Learning Segmentation for 3D Point Clouds](https://mlsanity.com/paper/2508.11265/) (2025)
- [Scalable Learning from Probability Measures with Mean Measure Quantization](https://mlsanity.com/paper/2502.04907/) (2025)
- [SE-Merging: A Self-Enhanced Approach for Dynamic Model Merging](https://mlsanity.com/paper/2506.18135/) (2025)
- [TPCL: Task Progressive Curriculum Learning for Robust Visual Question Answering](https://mlsanity.com/paper/2411.17292/) (2024)
- [Relation-Aware Slicing in Cross-Domain Alignment](https://mlsanity.com/paper/2507.13194/) (2025)
- [Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric](https://mlsanity.com/paper/2509.04089/) (2025)
- [Gradient Flow Convergence Guarantee for General Neural Network Architectures](https://mlsanity.com/paper/2509.23887/) (2025)
- [Designing Ambiguity Sets for Distributionally Robust Optimization Using Structural Causal Optimal Transport](https://mlsanity.com/paper/2510.00599/) (2025)
- [Simplifying Optimal Transport through Schatten-p Regularization](https://mlsanity.com/paper/2510.11910/) (2025)
- [Accelerated Sinkhorn Algorithms for Partial Optimal Transport](https://mlsanity.com/paper/2601.17196/) (2026)
- [PCA of probability measures: Sparse and Dense sampling regimes](https://mlsanity.com/paper/2602.02190/) (2026)
- [Gromov Wasserstein Optimal Transport for Semantic Correspondences](https://mlsanity.com/paper/2602.03105/) (2026)
- [Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks](https://mlsanity.com/paper/2602.09181/) (2026)
- [Move What Matters: Parameter-Efficient Domain Adaptation via Optimal Transport Flow for Collaborative Perception](https://mlsanity.com/paper/2602.11565/) (2026)
- [ViCLIP-OT: The First Foundation Vision-Language Model for Vietnamese Image-Text Retrieval with Optimal Transport](https://mlsanity.com/paper/2602.22678/) (2026)
- [Region-Graph Optimal Transport Routing for Mixture-of-Experts Whole-Slide Image Classification](https://mlsanity.com/paper/2604.07298/) (2026)
- [UG-UMRE: Uncertainty-Guided Modality Augmentation and Distributional Calibration for Unified Multimodal Relation Extraction](https://mlsanity.com/paper/2608.04949/) (2026)
- [SinkSLOT: Sinkhorn via Sparse Lifted Optimal Transport](https://mlsanity.com/paper/2608.28262/) (2026)
- [Optimal transport meets speech: a tutorial review](https://mlsanity.com/paper/2609.31787/) (2026)

## Abstract (arXiv)

Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable contributions of this classical optimization problem to machine learning. This paper is about where and how optimal transport is used in machine learning with a focus on the question of scalable optimal transport. We provide a comprehensive survey of optimal transport while ensuring an accessible presentation as permitted by the nature of the topic and the context. First, we explain the optimal transport background and introduce different flavors (i.e., mathematical formulations), properties, and notable applications. We then address the fundamental question of how to scale optimal transport to cope with the current demands of big and high dimensional data. We conduct a systematic analysis of the methods used in the literature for scaling OT and present the findings in a unified taxonomy. We conclude with presenting some open challenges and discussing potential future research directions. A live repository of related OT research papers is maintained in https://github.com/abdelwahed/OT_for_big_data.git