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Measurement Embedded Schr"odinger Bridge for Inverse Problems

arXiv 2407.04162 ↗First posted 23 May 2024eess.IV cs.CVcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image Schr"odinger Bridge (I2SB), which begins with the corrupted image, presents a promising alternative as a prior for addressing inverse problems. In this work, we introduce the Measurement Embedded Schr"odinger Bridge (MESB). MESB establishes Schr"odinger Bridges between the distribution of corrupted images and the distribution of clean images given observed measurements. Based on optimal transport theory, we derive the forward and backward processes of MESB. Through validation on diverse inverse problems, our proposed approach exhibits superior performance compared to existing Schr"odinger Bridge-based inverse problems solvers in both visual quality and quantitative metrics.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 14 of its 18 references that are in the map. First posted on arXiv 23 May 2024.

Builds on

14 of 18 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge24 May
  2. 2023I2SB: Image-to-Image Schr"odinger Bridge12 Feb
  3. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 9

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  3. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  4. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  5. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  6. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  7. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  8. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problemscited by 65
  9. 2022RPLHR-CT Dataset and Transformer Baseline for Volumetric Super-Resolution from CT Scanscited by 14

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  1. 2024Implicit Image-to-Image Schrodinger Bridge for Image Restoration
  2. 2022Conditional Simulation Using Diffusion Schr"odinger Bridges
  3. 2024Latent Schrodinger Bridge: Prompting Latent Diffusion for Fast Unpaired Image-to-Image Translation
  4. 2024Guided MRI Reconstruction via Schr"odinger Bridge
  5. 2025System-Embedded Diffusion Bridge Models
  6. 2025Acoustic Waveform Inversion with Image-to-Image Schr"odinger Bridges
  7. 2026Reflected Schr"odinger Bridge Matching
  8. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge