mlsanityData to 7 Oct 2026

Linearly Constrained Diffusion Implicit Models

arXiv 2411.00359 ↗First posted 1 Nov 2024cs.LG eess.IVcited by 1

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

Abstract (arXiv)

We introduce Linearly Constrained Diffusion Implicit Models (CDIM), a fast and accurate approach to solving noisy linear inverse problems using diffusion models. Traditional diffusion-based inverse methods rely on numerous projection steps to enforce measurement consistency in addition to unconditional denoising steps. CDIM achieves a 10-50x reduction in projection steps by dynamically adjusting the number and size of projection steps to align a residual measurement energy with its theoretical distribution under the forward diffusion process. This adaptive alignment preserves measurement consistency while substantially accelerating constrained inference. For noise-free linear inverse problems, CDIM exactly satisfies the measurement constraints with few projection steps, even when existing methods fail. We demonstrate CDIM's effectiveness across a range of applications, including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reprojection. Code and an interactive demo can be found on our project website.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 26 of its 44 references that are in the map. First posted on arXiv 1 Nov 2024.

Builds on

26 of 44 references.

Closest ancestors · 13

Same direction, newest first

  1. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMC13 Sep
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  3. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models27 May
  4. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution1 Sep
  5. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems15 Aug
  6. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  7. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  8. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  9. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problems19 Nov
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  11. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  12. 2022Denoising Diffusion Restoration Models27 Jan
1 more
  1. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 13

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  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. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  7. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 695
  8. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  9. 2016Learning in Implicit Generative Modelscited by 124
  10. 2024Constrained Synthesis with Projected Diffusion Modelscited by 83
  11. 2024Guidance with Spherical Gaussian Constraint for Conditional Diffusioncited by 69
  12. 2023Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generationcited by 51
1 more
  1. 2020Time-Travel Rephotographycited by 26

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Divergence-Free Diffusion Models for Incompressible Fluid Flowscited by 2

Similar, not cited

Close in wording, no citation either way

  1. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM
  2. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  3. 2025Diffusion models for inverse problems
  4. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models
  5. 2024CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problems
  6. 2025SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems
  7. 2024Enhancing and Accelerating Diffusion-Based Inverse Problem Solving through Measurements Optimization
  8. 2023Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling