mlsanityData to 7 Oct 2026

The data-driven Schroedinger bridge

arXiv 1806.01364 ↗First posted 4 Jun 2018math.OCcited by 26

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Abstract (arXiv)

Erwin Schroedinger posed, and to a large extent solved in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of the two distributions are available. A novel iterative procedure is proposed, inspired by Fortet-Sinkhorn type algorithms. Since only samples of the marginals are available, the new approach features constrained maximum likelihood estimation in place of the nonlinear boundary couplings, and importance sampling to propagate the functions varphi and hatvarphi solving the Schroedinger system. This method is well-suited to high-dimensional settings, where introducing grids leads to numerically unfeasible or unreliable methods. The methodology is illustrated in two applications: entropic interpolation of two-dimensional Gaussian mixtures, and the estimation of integrals through a variation of importance sampling.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 2; 2023: 6; 2024: 5; 2025: 6; 2026: 4.

26 papers.

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  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  2. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  3. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  4. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  5. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  6. 2023A mean-field games laboratory for generative modelingcited by 28
  7. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  8. 2022First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Datacited by 18
  9. 2023Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assemblycited by 10
  10. 2025Momentum Multi-Marginal Schr"odinger Bridge Matchingcited by 9
  11. 2024DPBridge: Latent Diffusion Bridge for Dense Predictioncited by 6
  12. 2026FLAC: Maximum Entropy RL via Kinetic Energy Regularized Bridge Matchingcited by 5
14 more
  1. 2023One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Modelscited by 4
  2. 2024Simplified Diffusion Schr"odinger Bridgecited by 4
  3. 2024Feedback Schr"odinger Bridge Matchingcited by 4
  4. 2025Oh SnapMMD! Forecasting Stochastic Dynamics Beyond the Schr"odinger Bridge's Endcited by 4
  5. 2025Branched Schr"odinger Bridge Matchingcited by 4
  6. 2023Path Structured Multimarginal Schr"odinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Softwarecited by 3
  7. 2024Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schr"odinger Bridge and Reaction-Diffusion PDEscited by 3
  8. 2025Forward Reverse Kernel Regression for the Schr"odinger bridge problemcited by 1
  9. 2025Incorporating Pre-trained Diffusion Models in Solving the Schr"odinger Bridge Problemcited by 1
  10. 2026Generalized Schr"odinger Bridge on Graphscited by 1
  11. 2026MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics datacited by 1
  12. 2024Control, Transport and Sampling: Towards Better Loss Designcited by 0
  13. 2025Statistical Analysis of the Sinkhorn Iterations for Two-Sample Schr"odinger Bridge Estimationcited by 0
  14. 2026Path-Space Mirror Descent for On-Policy Reinforcement Learning under the Generalized Schr"odinger Bridgecited by 0