mlsanityData to 13 Oct 2026

GSURE-Based Diffusion Model Training with Corrupted Data

arXiv 2305.13128 ↗First posted 22 May 2023eess.IV cs.CV cs.LGcited by 40

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have demonstrated impressive results in both data generation and downstream tasks such as inverse problems, text-based editing, classification, and more. However, training such models usually requires large amounts of clean signals which are often difficult or impossible to obtain. In this work, we propose a novel training technique for generative diffusion models based only on corrupted data. We introduce a loss function based on the Generalized Stein's Unbiased Risk Estimator (GSURE), and prove that under some conditions, it is equivalent to the training objective used in fully supervised diffusion models. We demonstrate our technique on face images as well as Magnetic Resonance Imaging (MRI), where the use of undersampled data significantly alleviates data collection costs. Our approach achieves generative performance comparable to its fully supervised counterpart without training on any clean signals. In addition, we deploy the resulting diffusion model in various downstream tasks beyond the degradation present in the training set, showcasing promising results.

Key facts. Cited by 40 papers in the map (data through 13 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 56 of its 74 references that are in the map. First posted on arXiv 22 May 2023.

Builds on

56 of 74 references.

Closest ancestors · 11

Same direction, newest first

  1. 2023MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer25 Mar
  2. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models28 Nov
  3. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models15 Jun
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  5. 2021Score-Based Generative Classifiers1 Oct
  6. 2021Score-based Generative Modeling in Latent Space10 Jun
  7. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  8. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  10. 2020Denoising Diffusion Implicit Models6 Oct
  11. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 45

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,656
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,023
  3. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,141
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,077
  5. 2014Deep Learning Face Attributes in the Wildcited by 3,686
  6. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,768
  7. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,732
  8. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,348
  9. 2022Imagic: Text-Based Real Image Editing with Diffusion Modelscited by 1,176
  10. 2022Human Motion Diffusion Modelcited by 1,067
  11. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,012
  12. 2022Denoising Diffusion Restoration Modelscited by 958
33 more
  1. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 529
  2. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 519
  3. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 467
  4. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 446
  5. 2022DiffuSeq: Sequence to Sequence Text Generation with Diffusion Modelscited by 444
  6. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 342
  7. 2021Score-based diffusion models for accelerated MRIcited by 309
  8. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 285
  9. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 275
  10. 2023SE(3) diffusion model with application to protein backbone generationcited by 218
  11. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 214
  12. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 131
  13. 2022Fast Unsupervised Brain Anomaly Detection and Segmentation with Diffusion Modelscited by 97
  14. 2022Lossy Compression with Gaussian Diffusioncited by 88
  15. 2019MisGAN: Learning from Incomplete Data with Generative Adversarial Networkscited by 75
  16. 2019RARE: Image Reconstruction using Deep Priors Learned without Ground Truthcited by 64
  17. 2022Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstructioncited by 64
  18. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  19. 2018Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networkscited by 53
  20. 2023DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Modelscited by 50
  21. 2018Unsupervised Learning with Stein's Unbiased Risk Estimatorcited by 47
  22. 2018Training Deep Learning Based Denoisers without Ground Truth Datacited by 43
  23. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Datacited by 40
  24. 2021Rethinking Deep Image Prior for Denoisingcited by 38
  25. 2021One-dimensional Deep Low-rank and Sparse Network for Accelerated MRIcited by 27
  26. 2022DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removalcited by 25
  27. 2019PILOT: Physics-Informed Learned Optimized Trajectories for Accelerated MRIcited by 24
  28. 2022Threat Model-Agnostic Adversarial Defense using Diffusion Modelscited by 24
  29. 2023Synthetic ECG Signal Generation using Probabilistic Diffusion Modelscited by 22
  30. 2018Training deep learning based image denoisers from undersampled measurements without ground truth and without image priorcited by 15
  31. 2020ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithmscited by 14
  32. 2021Image Restoration by Deep Projected GSUREcited by 8
  33. 2023Thompson Sampling with Diffusion Generative Priorcited by 7

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 6; 2024: 15; 2025: 15; 2026: 4.

40 papers.

Sort:

By area:

  1. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 157
  2. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  3. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
  4. 2025Synthetic Data Generation Using Large Language Models: Advances in Text and Codecited by 61
  5. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  6. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  7. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  8. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problemscited by 21
  9. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  10. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observationscited by 20
  11. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  12. 2025Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusioncited by 17
28 more
  1. 2025Diffusion models for inverse problemscited by 16
  2. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  3. 2023SMRD: SURE-based Robust MRI Reconstruction with Diffusion Modelscited by 15
  4. 2024Osmosis: RGBD Diffusion Prior for Underwater Image Restorationcited by 13
  5. 2024Adaptive Compressed Sensing with Diffusion-Based Posterior Samplingcited by 12
  6. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Imagescited by 12
  7. 2024MotionMix: Weakly-Supervised Diffusion for Controllable Motion Generationcited by 10
  8. 2024Solving Inverse Problems via Diffusion Optimal Controlcited by 8
  9. 2025Measurement Score-Based Diffusion Modelcited by 8
  10. 2025Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generationcited by 7
  11. 2024Amortized Posterior Sampling with Diffusion Prior Distillationcited by 6
  12. 2025DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximizationcited by 6
  13. 2023Nested Diffusion Processes for Anytime Image Generationcited by 5
  14. 2025Inverse Flow and Consistency Modelscited by 5
  15. 2025Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolantscited by 5
  16. 2025Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstructioncited by 4
  17. 2025Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Modelscited by 4
  18. 2026Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Roboticscited by 4
  19. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3
  20. 2025Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurementscited by 3
  21. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Methodcited by 2
  22. 2025Double Blind Imaging with Generative Modelingcited by 1
  23. 2025Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Datacited by 0
  24. 2025What is Adversarial Training for Diffusion Models?cited by 0
  25. 2025UPMRI: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matchingcited by 0
  26. 2026Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasetscited by 0
  27. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Supportcited by 0
  28. 2026Ambient Discrete Diffusion: Using the Wrong Data at the Right Time for Data Efficient Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structure
  2. 2024GUD: Generation with Unified Diffusion
  3. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Survey
  4. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality
  5. 2025Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study
  6. 2023How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control
  7. 2023Reflected Diffusion Models
  8. 2023Unmasking Bias in Diffusion Model Training