mlsanityData to 14 Oct 2026

DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization

arXiv 2510.12691 ↗First posted 14 Oct 2025cs.LG cs.AI cs.CVcited by 6

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

Abstract (arXiv)

Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for training diffusion models with Expectation-Maximization (EM) from corrupted data. Our proposed method, DiffEM, utilizes conditional diffusion models to reconstruct clean data from observations in the E-step, and then uses the reconstructed data to refine the conditional diffusion model in the M-step. Theoretically, we provide monotonic convergence guarantees for the DiffEM iteration, assuming appropriate statistical conditions. We demonstrate the effectiveness of our approach through experiments on various image reconstruction tasks.

Key facts. Cited by 6 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 38 of its 50 references that are in the map. First posted on arXiv 14 Oct 2025.

Builds on

38 of 50 references.

Closest ancestors · 7

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  2. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations1 Jul
  3. 2024Learning Diffusion Priors from Observations by Expectation Maximization22 May
  4. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data13 Mar
  5. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data2 May
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  7. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2023DINOv2: Learning Robust Visual Features without Supervisioncited by 7,974
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2016Improved Techniques for Training GANscited by 2,970
  7. 2021Palette: Image-to-Image Diffusion Modelscited by 1,300
  8. 2023Extracting Training Data from Diffusion Modelscited by 732
  9. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 635
  10. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  11. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  12. 2022Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Modelscited by 424
19 more
  1. 2023Understanding and Mitigating Copying in Diffusion Modelscited by 209
  2. 2023Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion modelscited by 205
  3. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  4. 2015On Wasserstein Two Sample Testing and Related Families of Nonparametric Testscited by 166
  5. 2019Effectively Unbiased FID and Inception Score and where to find themcited by 165
  6. 2023Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Modelscited by 133
  7. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  8. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 63
  9. 2024Optimal score estimation via empirical Bayes smoothingcited by 61
  10. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  11. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptionscited by 47
  12. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  13. 2024Learning general Gaussian mixtures with efficient score matchingcited by 44
  14. 2024Learning Mixtures of Gaussians Using Diffusion Modelscited by 42
  15. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  16. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 34
  17. 2024From optimal score matching to optimal samplingcited by 28
  18. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  19. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 5.

6 papers.

  1. 2025Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolantscited by 6
  2. 2026Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Roboticscited by 4
  3. 2026Ambient Dataloops: Generative Models for Dataset Refinementcited by 2
  4. 2026SURF: Separation via Unsupervised Remixing Flowcited by 0
  5. 2026Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputationcited by 0
  6. 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. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
  2. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
  3. 2023Removing Structured Noise with Diffusion Models
  4. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models
  5. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Images
  6. 2024Blind Inversion using Latent Diffusion Priors
  7. 2025Learning Single Index Models with Diffusion Priors
  8. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems