mlsanityData to 14 Oct 2026

I2SB: Image-to-Image Schr"odinger Bridge

arXiv 2302.05872 ↗First posted 12 Feb 2023cs.CV cs.LG stat.MLcited by 218

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We propose Image-to-Image Schr"odinger Bridge (I2SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for image restoration, as the degraded images are structurally informative priors for reconstructing the clean images. I2SB belongs to a tractable class of Schr"odinger bridge, the nonlinear extension to score-based models, whose marginal distributions can be computed analytically given boundary pairs. This results in a simulation-free framework for nonlinear diffusions, where the I2SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I2SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I2SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I2SB matches the performance of inverse methods that additionally require the knowledge of the corruption operators. Our work opens up new algorithmic opportunities for developing efficient nonlinear diffusion models on a large scale. scale. Project page and codes: https://i2sb.github.io/

Key facts. Cited by 218 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 45 of its 79 references that are in the map. First posted on arXiv 12 Feb 2023.

Builds on

45 of 79 references.

Closest ancestors · 13

Same direction, newest first

  1. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  2. 2022Conditional Simulation Using Diffusion Schr"odinger Bridges27 Feb
  3. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents2 Jan
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  5. 2021Score-based Generative Modeling in Latent Space10 Jun
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  7. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  8. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct
  12. 2020Denoising Diffusion Probabilistic Models19 Jun
1 more
  1. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 32

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  5. 2022Flow Matching for Generative Modelingcited by 5,702
  6. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,527
  7. 2018Neural Ordinary Differential Equationscited by 3,779
  8. 2014Conditional Generative Adversarial Netscited by 2,162
  9. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,908
  10. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,300
20 more
  1. 2021Transformers in Vision: A Surveycited by 1,013
  2. 2022Denoising Diffusion Restoration Modelscited by 963
  3. 2018Multimodal Unsupervised Image-to-Image Translationcited by 795
  4. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  5. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 583
  6. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  7. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 508
  8. 2022Diffusion Models for Adversarial Purificationcited by 476
  9. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  10. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
  11. 2021Deblurring via Stochastic Refinementcited by 249
  12. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 219
  13. 2022Dual Diffusion Implicit Bridges for Image-to-Image Translationcited by 213
  14. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 181
  15. 2022Pretraining is All You Need for Image-to-Image Translationcited by 160
  16. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 141
  17. 2020Contextual Residual Aggregation for Ultra High-Resolution Image Inpaintingcited by 124
  18. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  19. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Modelscited by 47
  20. 2017Pixel Recursive Super Resolutioncited by 44

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 28; 2024: 67; 2025: 69; 2026: 54.

218 papers.

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  1. 2023ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shiftingcited by 365
  2. 2023UniControl: A Unified Diffusion Model for Controllable Visual Generation In the Wildcited by 200
  3. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  4. 2023Denoising Diffusion Bridge Modelscited by 178
  5. 2023Fast Training of Diffusion Models with Masked Transformerscited by 176
  6. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 165
  7. 2023Diffusion Schr"odinger Bridge Matchingcited by 153
  8. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 150
  9. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  10. 2023CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Samplingcited by 129
  11. 2024Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Modelscited by 114
  12. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
38 more
  1. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 83
  2. 2024Diffusion Models in Low-Level Vision: A Surveycited by 74
  3. 2024Selective Hourglass Mapping for Universal Image Restoration Based on Diffusion Modelcited by 73
  4. 2023Residual Denoising Diffusion Modelscited by 69
  5. 2023On the Generalization Properties of Diffusion Modelscited by 68
  6. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 66
  7. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 64
  8. 2024No Training, No Problem: Rethinking Classifier-Free Guidance for Diffusion Modelscited by 53
  9. 2024Diffusion Bridge Implicit Modelscited by 49
  10. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  11. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 43
  12. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 42
  13. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  14. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  15. 2024Rethinking Score Distillation as a Bridge Between Image Distributionscited by 38
  16. 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
  17. 2025FlowTok: Flowing Seamlessly Across Text and Image Tokenscited by 33
  18. 2023Accurate transition state generation with an object-aware equivariant elementary reaction diffusion modelcited by 30
  19. 2023Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesiscited by 30
  20. 2023DiffCR: A Fast Conditional Diffusion Framework for Cloud Removal from Optical Satellite Imagescited by 27
  21. 2024DreamFlow: High-Quality Text-to-3D Generation by Approximating Probability Flowcited by 26
  22. 2023Generative Modeling with Phase Stochastic Bridgescited by 25
  23. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 24
  24. 2024Consistency Diffusion Bridge Modelscited by 23
  25. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  26. 2024DreamSampler: Unifying Diffusion Sampling and Score Distillation for Image Manipulationcited by 22
  27. 2024LiteVAE: Lightweight and Efficient Variational Autoencoders for Latent Diffusion Modelscited by 22
  28. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  29. 2025Adjoint Schr"odinger Bridge Samplercited by 21
  30. 2024The Landscape of Unfolding with Machine Learningcited by 20
  31. 2024Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problemscited by 20
  32. 2025UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Controlcited by 20
  33. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlocited by 20
  34. 2023Resfusion: Denoising Diffusion Probabilistic Models for Image Restoration Based on Prior Residual Noisecited by 19
  35. 2024ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Imagescited by 19
  36. 2025h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transformcited by 19
  37. 2024Bidirectional Consistency Modelscited by 18
  38. 2024P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoisingcited by 18

50 most cited of 218 All 218 (JSON)

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  1. 2024Latent Schrodinger Bridge: Prompting Latent Diffusion for Fast Unpaired Image-to-Image Translation
  2. 2024Reflected Schr"odinger Bridge for Constrained Generative Modeling
  3. 2024Sch"odinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders
  4. 2026Reflected Schr"odinger Bridge Matching
  5. 2023A Unified Conditional Framework for Diffusion-based Image Restoration
  6. 2025IRBridge: Solving Image Restoration Bridge with Pre-trained Generative Diffusion Models
  7. 2026Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models
  8. 2026LightSBB-M: Bridging Schr"odinger and Bass for Generative Diffusion Modeling