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Multi-marginal optimal transport: theory and applications

arXiv 1406.0026 ↗First posted 30 May 2014math.AP math.OCcited by 41

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Abstract (arXiv)

Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging applications. Here, we survey this problem, addressing fundamental theoretical questions including the uniqueness and structure of solutions. The (partial) answers to these questions uncover a surprising divergence from the classical two marginal setting, and reflect a delicate dependence on the cost function. We go one to describe two applications of the multi-marginal problem.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 May 2014.

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Citing papers per year: 2021: 4; 2022: 7; 2023: 8; 2024: 8; 2025: 8; 2026: 6.

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  1. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  2. 2023Hierarchical Multi-Marginal Optimal Transport for Network Alignmentcited by 24
  3. 2025DecAlign: Hierarchical Cross-Modal Alignment for Decoupled Multimodal Representation Learningcited by 23
  4. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  5. 2023Projected Langevin dynamics and a gradient flow for entropic optimal transportcited by 17
  6. 2023Multimarginal generative modeling with stochastic interpolantscited by 17
  7. 2023Data Valuation and Detections in Federated Learningcited by 17
  8. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  9. 2024LinSATNet: The Positive Linear Satisfiability Neural Networkscited by 16
  10. 2023Causal Optimal Transport of Abstractionscited by 13
  11. 2022An Optimal Transport Approach to Personalized Federated Learningcited by 12
  12. 2022Convergence Rates for Regularized Optimal Transport via Quantizationcited by 11
29 more
  1. 2025Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Pointscited by 11
  2. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  3. 2021On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexitycited by 8
  4. 2024Contrasting Multiple Representations with the Multi-Marginal Matching Gapcited by 8
  5. 2025Your contrastive learning problem is secretly a distribution alignment problemcited by 6
  6. 2025Longitudinal Flow Matching for Trajectory Modelingcited by 6
  7. 2021Sliced Multi-Marginal Optimal Transportcited by 5
  8. 2022Mirror Sinkhorn: Fast Online Optimization on Transport Polytopescited by 5
  9. 2024On Probabilistic Embeddings in Optimal Dimension Reductioncited by 5
  10. 2021Order Constraints in Optimal Transportcited by 4
  11. 2021Matching for causal effects via multimarginal unbalanced optimal transportcited by 4
  12. 2025Unsupervised Anomaly Detection through Mass Repulsing Optimal Transportcited by 4
  13. 2023Path Structured Multimarginal Schr"odinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Softwarecited by 3
  14. 2024A Sinkhorn-type Algorithm for Constrained Optimal Transportcited by 3
  15. 2024Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridgecited by 3
  16. 2023A New Perspective On Denoising Based On Optimal Transportcited by 2
  17. 2025Neural Estimation for Scaling Entropic Multimarginal Optimal Transportcited by 2
  18. 2022The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splinescited by 1
  19. 2024Sinkhorn Algorithm for Sequentially Composed Optimal Transportscited by 1
  20. 2025Optimal Multimarginal Schr"odinger Bridge: Minimum Spanning Tree over Measure-valued Verticescited by 1
  21. 2022Approximative Algorithms for Multi-Marginal Optimal Transport and Free-Support Wasserstein Barycenterscited by 0
  22. 2024Collision-based Dynamics for Multi-Marginal Optimal Transportcited by 0
  23. 2025Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learningcited by 0
  24. 2026HOT-POT: Optimal Transport for Sparse Stereo Matchingcited by 0
  25. 2026A Unified Kantorovich Duality for Multimarginal Optimal Transportcited by 0
  26. 2026Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocationcited by 0
  27. 2026Optimal and Scalable MAPF via Multi-Marginal Optimal Transport and Schr"odinger Bridgescited by 0
  28. 2026Path-independent Flow Matching for Multi-parameter Generative Dynamicscited by 0
  29. 2026Fast A/B/n Testing: Exact Multi-Policy Comparison via Tree-Coupled Feedback Sharingcited by 0