mlsanityData to 7 Oct 2026

Learning Gradually Non-convex Image Priors Using Score Matching

arXiv 2302.10502 ↗First posted 21 Feb 2023cs.LG cs.CVcited by 4

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

Abstract (arXiv)

In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy -- becomes convex. Consequently, denoising score-based models essentially follow a graduated non-convexity heuristic. We apply this framework to learning generalized Fields of Experts image priors that approximate the joint density of noisy images and their associated variances. These priors can be easily incorporated into existing optimization algorithms for solving inverse problems and naturally implement a fast and robust graduated non-convexity mechanism.

Key facts. Cited by 4 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 18 of its 31 references that are in the map. First posted on arXiv 21 Feb 2023.

Builds on

18 of 31 references.

References · 18

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  9. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  10. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  11. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 340
  12. 2020AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradientscited by 282
6 more
  1. 2022Continuous diffusion for categorical datacited by 202
  2. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 194
  3. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  4. 2020Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constantcited by 25
  5. 2014Insights into analysis operator learning: From patch-based sparse models to higher-order MRFscited by 18
  6. 2018Lifting Layers: Analysis and Applicationscited by 4

Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 1; 2025: 1.

4 papers.

  1. 2023Score-Based Generative Models for PET Image Reconstructioncited by 22
  2. 2025Learning normalized image densities via dual score matchingcited by 17
  3. 2023Product of Gaussian Mixture Diffusion Modelscited by 6
  4. 2024Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework
  2. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantification
  3. 2026Learning Normalized Energy Models for Linear Inverse Problems
  4. 2025Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
  5. 2025Optimizing Input of Denoising Score Matching is Biased Towards Higher Score Norm
  6. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging
  7. 2025Noise Conditional Variational Score Distillation
  8. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridges