mlsanityData to 14 Oct 2026

Incorporating Pre-trained Diffusion Models in Solving the Schr"odinger Bridge Problem

arXiv 2508.18095 ↗First posted 25 Aug 2025cs.CV cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

This paper aims to unify Score-based Generative Models (SGMs), also known as Diffusion models, and the Schr"odinger Bridge (SB) problem through three reparameterization techniques: Iterative Proportional Mean-Matching (IPMM), Iterative Proportional Terminus-Matching (IPTM), and Iterative Proportional Flow-Matching (IPFM). These techniques significantly accelerate and stabilize the training of SB-based models. Furthermore, the paper introduces novel initialization strategies that use pre-trained SGMs to effectively train SB-based models. By using SGMs as initialization, we leverage the advantages of both SB-based models and SGMs, ensuring efficient training of SB-based models and further improving the performance of SGMs. Extensive experiments demonstrate the significant effectiveness and improvements of the proposed methods. We believe this work contributes to and paves the way for future research on generative models.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 63 of its 81 references that are in the map. First posted on arXiv 25 Aug 2025.

Builds on

63 of 81 references.

Closest ancestors · 22

Same direction, newest first

  1. 2024A Closer Look at Time Steps is Worthy of Triple Speed-Up for Diffusion Model Training27 May
  2. 2024Adversarial Schr"odinger Bridge Matching23 May
  3. 2023Denoising Diffusion Bridge Models29 Sep
  4. 2023Common Diffusion Noise Schedules and Sample Steps are Flawed15 May
  5. 2023Diffusion Schr"odinger Bridge Matching29 Mar
  6. 2023Efficient Diffusion Training via Min-SNR Weighting Strategy16 Mar
  7. 2023I2SB: Image-to-Image Schr"odinger Bridge12 Feb
  8. 2023Simple diffusion: End-to-end diffusion for high resolution images26 Jan
  9. 2023On the Importance of Noise Scheduling for Diffusion Models26 Jan
  10. 2022Scalable Diffusion Models with Transformers19 Dec
  11. 2022f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation10 Oct
  12. 2022Classifier-Free Diffusion Guidance26 Jul
10 more
  1. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  3. 2022Improved Vector Quantized Diffusion Models31 May
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  5. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesis29 Nov
  6. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  7. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  8. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  10. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 41

  1. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  3. 2022Flow Matching for Generative Modelingcited by 5,702
  4. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,527
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2018Neural Ordinary Differential Equationscited by 3,779
  7. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  8. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  9. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,581
  10. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  11. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  12. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
29 more
  1. 2022MaskGIT: Masked Generative Image Transformercited by 1,099
  2. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,098
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  4. 2022eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoiserscited by 931
  5. 2024WorldSimBench: Towards Video Generation Models as World Simulatorscited by 881
  6. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  7. 2017DualGAN: Unsupervised Dual Learning for Image-to-Image Translationcited by 310
  8. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
  9. 2022BBDM: Image-to-image Translation with Brownian Bridge Diffusion Modelscited by 225
  10. 2019Few-Shot Unsupervised Image-to-Image Translationcited by 222
  11. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 219
  12. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
  13. 2019U-GAT-IT: Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translationcited by 186
  14. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 165
  15. 2016Dual Learning for Machine Translationcited by 148
  16. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 141
  17. 2022Neural Optimal Transportcited by 126
  18. 2016Unsupervised Cross-Domain Image Generationcited by 125
  19. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 123
  20. 2021Score-based Generative Neural Networks for Large-Scale Optimal Transportcited by 60
  21. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  22. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 50
  23. 2023VolumeDiffusion: Flexible Text-to-3D Generation with Efficient Volumetric Encodercited by 39
  24. 2015Entropic and displacement interpolation: a computational approach using the Hilbert metriccited by 34
  25. 2023Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesiscited by 30
  26. 2018The data-driven Schroedinger bridgecited by 26
  27. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  28. 2023Light Schr"odinger Bridgecited by 18
  29. 2024BM2: Coupled Schr"odinger Bridge Matchingcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Deterministic Decomposition of Stochastic Generative Dynamicscited by 0

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  6. 2024Sch"odinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders
  7. 2026Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schr"odinger Bridge Matching
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