mlsanityData to 7 Oct 2026

Conditional Simulation Using Diffusion Schr"odinger Bridges

arXiv 2202.13460 ↗First posted 27 Feb 2022stat.ML cs.LGcited by 58

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusion models have recently emerged as a powerful class of generative models. They provide state-of-the-art results, not only for unconditional simulation, but also when used to solve conditional simulation problems arising in a wide range of inverse problems. A limitation of these models is that they are computationally intensive at generation time as they require simulating a diffusion process over a long time horizon. When performing unconditional simulation, a Schr"odinger bridge formulation of generative modeling leads to a theoretically grounded algorithm shortening generation time which is complementary to other proposed acceleration techniques. We extend the Schr"odinger bridge framework to conditional simulation. We demonstrate this novel methodology on various applications including image super-resolution, optimal filtering for state-space models and the refinement of pre-trained networks. Our code can be found at https://github.com/vdeborto/cdsb.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 34 of its 60 references that are in the map. First posted on arXiv 27 Feb 2022.

Builds on

34 of 60 references.

Closest ancestors · 15

Same direction, newest first

  1. 2022Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders19 Feb
  2. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  3. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  4. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  5. 2021Conditional Image Generation with Score-Based Diffusion Models26 Nov
  6. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  7. 2021Variational Diffusion Models1 Jul
  8. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  9. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
3 more
  1. 2020Denoising Diffusion Implicit Models6 Oct
  2. 2020Denoising Diffusion Probabilistic Models19 Jun
  3. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 19

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  3. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  4. 2022Denoising Diffusion Restoration Modelscited by 951
  5. 2018Computational Optimal Transportcited by 765
  6. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  7. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  8. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  9. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 306
  10. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  11. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  12. 2020SRFlow: Learning the Super-Resolution Space with Normalizing Flowcited by 209
7 more
  1. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  2. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  3. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  4. 2022Conditional Diffusion Probabilistic Model for Speech Enhancementcited by 132
  5. 2019Coupling techniques for nonlinear ensemble filteringcited by 48
  6. 2019HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inferencecited by 31
  7. 2020A gradient descent perspective on Sinkhorncited by 24

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 21; 2024: 14; 2025: 12; 2026: 4.

58 papers.

Sort:

By area:

  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2022Diffusion Models in Vision: A Surveycited by 1,008
  3. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  4. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  5. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 214
  6. 2023Denoising Diffusion Bridge Modelscited by 171
  7. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  8. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  9. 2023Stochastic interpolants with data-dependent couplingscited by 94
  10. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  11. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  12. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
38 more
  1. 2022Compositional Score Modeling for Simulation-based Inferencecited by 46
  2. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Modelscited by 45
  3. 2023Deep Momentum Multi-Marginal Schr"odinger Bridgecited by 40
  4. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  5. 2022Unifying Generative Models with GFlowNets and Beyondcited by 24
  6. 2023Generative Modeling with Phase Stochastic Bridgescited by 24
  7. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correctioncited by 23
  8. 2023Distribution learning via neural differential equations: a nonparametric statistical perspectivecited by 22
  9. 2024Consistency Diffusion Bridge Modelscited by 22
  10. 2023Augmented Bridge Matchingcited by 21
  11. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  12. 2024Conditional sampling within generative diffusion modelscited by 18
  13. 2024Score-based generative models are provably robust: an uncertainty quantification perspectivecited by 14
  14. 2023Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimationcited by 13
  15. 2025FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilationcited by 13
  16. 2025Inverse Bridge Matching Distillationcited by 13
  17. 2022An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithmscited by 11
  18. 2024Conditioning diffusion models by explicit forward-backward bridgingcited by 11
  19. 2025Learning Enhanced Ensemble Filterscited by 11
  20. 2023Nonlinear Filtering with Brenier Optimal Transport Mapscited by 10
  21. 2023A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEscited by 9
  22. 2023Transport with Support: Data-Conditional Diffusion Bridgescited by 9
  23. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  24. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  25. 2023Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Modelscited by 8
  26. 2024Soft-constrained Schrodinger Bridge: a Stochastic Control Approachcited by 8
  27. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  28. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 5
  29. 2024Posterior sampling via Langevin dynamics based on generative priorscited by 5
  30. 2025Fast filtering of non-Gaussian models using Amortized Optimal Transport Mapscited by 4
  31. 2024Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transportcited by 2
  32. 2024Schr"odinger bridge based deep conditional generative learningcited by 2
  33. 2025Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Mapscited by 2
  34. 2024Generative Conditional Distributions by Neural (Entropic) Optimal Transportcited by 1
  35. 2025A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarioscited by 1
  36. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  37. 2024Mirror Bridges Between Probability Measurescited by 0
  38. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0

50 most cited of 58 All 58 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2026Foundations of Schr"odinger Bridges for Generative Modeling
  2. 2024Reflected Schr"odinger Bridge for Constrained Generative Modeling
  3. 2024Implicit Image-to-Image Schrodinger Bridge for Image Restoration
  4. 2024Sch"odinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders
  5. 2024Simplified Diffusion Schr"odinger Bridge
  6. 2024Measurement Embedded Schr"odinger Bridge for Inverse Problems
  7. 2025Finding Local Diffusion Schr"odinger Bridge using Kolmogorov-Arnold Network
  8. 2026Reflected Schr"odinger Bridge Matching