mlsanityData to 14 Oct 2026

Measurement Score-Based Diffusion Model

arXiv 2505.11853 ↗First posted 17 May 2025eess.IV cs.LGcited by 8

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce the Measurement Score-based diffusion Model (MSM), a novel framework that learns partial measurement scores using only noisy and subsampled measurements. MSM models the distribution of full measurements as an expectation over partial scores induced by randomized subsampling. To make the MSM representation computationally efficient, we also develop a stochastic sampling algorithm that generates full images by using a randomly selected subset of partial scores at each step. We additionally propose a new posterior sampling method for solving inverse problems that reconstructs images using these partial scores. We provide a theoretical analysis that bounds the Kullback-Leibler divergence between the distributions induced by full and stochastic sampling, establishing the accuracy of the proposed algorithm. We demonstrate the effectiveness of MSM on natural images and multi-coil MRI, showing that it can generate high-quality images and solve inverse problems -- all without access to clean training data. Code is available at https://github.com/wustl-cig/MSM.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 31 of its 45 references that are in the map. First posted on arXiv 17 May 2025.

Builds on

31 of 45 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method15 Oct
  2. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations1 Jul
  3. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data13 Mar
  4. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data2 May
  5. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 25

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  7. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  8. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  9. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 183
  10. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  11. 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
  12. 2013Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programmingcited by 75
13 more
  1. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  2. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  3. 2023DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Modelscited by 51
  4. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  5. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  6. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  7. 2022A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noisecited by 30
  8. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  9. 2024Conditioning non-linear and infinite-dimensional diffusion processescited by 15
  10. 2022Clean self-supervised MRI reconstruction from noisy, sub-sampled training data with Robust SSDUcited by 10
  11. 2022SPICER: Self-Supervised Learning for MRI with Automatic Coil Sensitivity Estimation and Reconstructioncited by 10
  12. 2022A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problemscited by 9
  13. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Modelscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 6.

8 papers.

  1. 2026Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Roboticscited by 4
  2. 2025Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurementscited by 3
  3. 2025Measurement Score-Based MRI Reconstruction with Automatic Coil Sensitivity Estimationcited by 0
  4. 2026Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusionscited by 0
  5. 2026Trajectory Constraints for Imaging Inverse Problemscited by 0
  6. 2026CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flowcited by 0
  7. 2026Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimatescited by 0
  8. 2026Ambient Discrete Diffusion: Using the Wrong Data at the Right Time for Data Efficient Learningcited by 0

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  2. 2022Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction
  3. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
  4. 2023Score-based Diffusion Models for Bayesian Image Reconstruction
  5. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging
  6. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  7. 2025Learning Single Index Models with Diffusion Priors
  8. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements