mlsanityData to 7 Oct 2026

Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters

arXiv 2305.16557 ↗First posted 26 May 2023stat.ML cs.LG math.PRcited by 16

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Abstract (arXiv)

Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a tree-structured quadratic cost, i.e., a function that can be written as a sum of pairwise cost functions between the nodes of a tree. To address this problem, we develop Tree-based Diffusion Schr"odinger Bridge (TreeDSB), an extension of the Diffusion Schr"odinger Bridge (DSB) algorithm. TreeDSB corresponds to a dynamic and continuous state-space counterpart of the multimarginal Sinkhorn algorithm. A notable use case of our methodology is to compute Wasserstein barycenters which can be recast as the solution of a mOT problem on a star-shaped tree. We demonstrate that our methodology can be applied in high-dimensional settings such as image interpolation and Bayesian fusion.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 35 of its 82 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

35 of 82 references.

References · 35

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  8. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
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  10. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  11. 2013Fast Computation of Wasserstein Barycenterscited by 216
  12. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
23 more
  1. 2019Optimal transport mapping via input convex neural networkscited by 202
  2. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  3. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  4. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  5. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  6. 2020Deep Shells: Unsupervised Shape Correspondence with Optimal Transportcited by 74
  7. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
  8. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 49
  9. 2015Scalable Bayes via Barycenter in Wasserstein Spacecited by 44
  10. 2023Deep Momentum Multi-Marginal Schr"odinger Bridgecited by 40
  11. 2017Optimal Transport for Diffeomorphic Registrationcited by 39
  12. 2019An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithmcited by 38
  13. 2017Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learningcited by 34
  14. 2020Continuous Regularized Wasserstein Barycenterscited by 32
  15. 2018Stochastic Wasserstein Barycenterscited by 25
  16. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  17. 2020Estimating Barycenters of Measures in High Dimensionscited by 18
  18. 2018Measure-valued spline curves: an optimal transport viewpointcited by 17
  19. 2017Parallel Streaming Wasserstein Barycenterscited by 14
  20. 2016Robust transport over networkscited by 10
  21. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
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  23. 2020Variational Wasserstein Barycenters for Geometric Clusteringcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 6; 2026: 4.

16 papers.

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  1. 2023Multimarginal generative modeling with stochastic interpolantscited by 17
  2. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  3. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  4. 2025Distribution Prototype Diffusion Learning for Open-set Supervised Anomaly Detectioncited by 10
  5. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  6. 2024DPBridge: Latent Diffusion Bridge for Dense Predictioncited by 6
  7. 2025Branched Schr"odinger Bridge Matchingcited by 4
  8. 2024Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridgecited by 3
  9. 2025Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysiscited by 2
  10. 2025Neural Estimation for Scaling Entropic Multimarginal Optimal Transportcited by 2
  11. 2025Schr"odinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentrescited by 2
  12. 2026Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshotscited by 2
4 more
  1. 2025Optimal Multimarginal Schr"odinger Bridge: Minimum Spanning Tree over Measure-valued Verticescited by 1
  2. 2026Twisted Schr"odinger Bridge Matchingcited by 1
  3. 2026Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocationcited by 0
  4. 2026Unsupervised Domain Adaptation for Enhanced Radiometer Image Precipitation Estimation using Conditional Flow Matchingcited by 0