mlsanityData to 7 Oct 2026

An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations

arXiv 2407.01014 ↗First posted 1 Jul 2024cs.CVcited by 20

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

Abstract (arXiv)

Diffusion models excel in solving imaging inverse problems due to their ability to model complex image priors. However, their reliance on large, clean datasets for training limits their practical use where clean data is scarce. In this paper, we propose EMDiffusion, an expectation-maximization (EM) approach to train diffusion models from corrupted observations. Our method alternates between reconstructing clean images from corrupted data using a known diffusion model (E-step) and refining diffusion model weights based on these reconstructions (M-step). This iterative process leads the learned diffusion model to gradually converge to the true clean data distribution. We validate our method through extensive experiments on diverse computational imaging tasks, including random inpainting, denoising, and deblurring, achieving new state-of-the-art performance.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 43 of its 61 references that are in the map. First posted on arXiv 1 Jul 2024.

Builds on

43 of 61 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  2. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data2 May
  3. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  5. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  6. 2022Denoising Diffusion Restoration Models27 Jan
  7. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 36

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  8. 2021Zero-Shot Text-to-Image Generationcited by 4,276
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  10. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  12. 2016Variational Inference: A Review for Statisticianscited by 1,466
24 more
  1. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  2. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  4. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  5. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  6. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  7. 2021Score-based diffusion models for accelerated MRIcited by 308
  8. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  9. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 274
  10. 2022Diffusion models as plug-and-play priorscited by 230
  11. 2022RenderDiffusion: Image Diffusion for 3D Reconstruction, Inpainting and Generationcited by 162
  12. 2023Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervisioncited by 112
  13. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  14. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimationcited by 95
  15. 2021Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fieldscited by 69
  16. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  17. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  18. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  19. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  20. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  21. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  22. 2021DuDoTrans: Dual-Domain Transformer Provides More Attention for Sinogram Restoration in Sparse-View CT Reconstructioncited by 12
  23. 2022alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extractioncited by 9
  24. 2023Recovering a Molecule's 3D Dynamics from Liquid-phase Electron Microscopy Moviescited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 12; 2026: 5.

20 papers.

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  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  2. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  3. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  4. 2025Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusioncited by 17
  5. 2025Diffusion models for inverse problemscited by 15
  6. 2025Stochastic Forward-Backward Deconvolution: Training Diffusion Models with Finite Noisy Datasetscited by 11
  7. 2025Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generationcited by 7
  8. 2025Measurement Score-Based Diffusion Modelcited by 7
  9. 2025DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximizationcited by 6
  10. 2025Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolantscited by 5
  11. 2026Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Roboticscited by 4
  12. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Methodcited by 2
8 more
  1. 2025SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samplescited by 2
  2. 2026Ambient Dataloops: Generative Models for Dataset Refinementcited by 2
  3. 2025SFBD Flow: A Continuous-Optimization Framework for Training Diffusion Models with Noisy Samplescited by 1
  4. 2025Bimanual 3D Hand Motion and Articulation Forecasting in Everyday Imagescited by 1
  5. 2026Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Datacited by 1
  6. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observationcited by 1
  7. 2025Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Datacited by 0
  8. 2026Priors learned from legacy reconstructions inherit undetectable overconfidencecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution
  2. 2024Learning Diffusion Priors from Observations by Expectation Maximization
  3. 2024Blind Inversion using Latent Diffusion Priors
  4. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Images
  5. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models
  6. 2025A Mixture-Based Framework for Guiding Diffusion Models
  7. 2025Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements
  8. 2024EM Distillation for One-step Diffusion Models