mlsanityData to 7 Oct 2026

A survey of the Schr"odinger problem and some of its connections with optimal transport

arXiv 1308.0215 ↗First posted 1 Aug 2013math.PR math.FA math.OCcited by 286

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Cited by 80 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

This article is aimed at presenting the Schr"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr"odinger problem. We also give a survey of the related literature. In addition, some new results are proved.

Key facts. Cited by 286 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Aug 2013.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 18; 2023: 35; 2024: 58; 2025: 71; 2026: 92.

286 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  4. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  5. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  6. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 214
  7. 2022Dual Diffusion Implicit Bridges for Image-to-Image Translationcited by 212
  8. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  9. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  10. 2023Denoising Diffusion Samplerscited by 144
  11. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  12. 2022Neural Optimal Transportcited by 123
38 more
  1. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  2. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  3. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  4. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  5. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  6. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  7. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  8. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 65
  9. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  10. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 61
  11. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  12. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  13. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  14. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  15. 2022Deep Generalized Schr"odinger Bridgecited by 47
  16. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  17. 2024Light and Optimal Schr"odinger Bridge Matchingcited by 45
  18. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  19. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  20. 2023Aligned Diffusion Schr"odinger Bridgescited by 38
  21. 2024Rethinking Score Distillation as a Bridge Between Image Distributionscited by 36
  22. 2023RetroBridge: Modeling Retrosynthesis with Markov Bridgescited by 35
  23. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  24. 2021Towards a mathematical theory of trajectory inferencecited by 31
  25. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 30
  26. 2023A mean-field games laboratory for generative modelingcited by 28
  27. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  28. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  29. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  30. 2024DreamFlow: High-Quality Text-to-3D Generation by Approximating Probability Flowcited by 26
  31. 2024Multi-marginal Schr"odinger Bridges with Iterative Reference Refinementcited by 26
  32. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 25
  33. 2022Unifying Generative Models with GFlowNets and Beyondcited by 24
  34. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  35. 2023Augmented Bridge Matchingcited by 21
  36. 2024Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformationcited by 21
  37. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  38. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19

50 most cited of 286 All 286 (JSON)