mlsanityData to 7 Oct 2026

Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems

arXiv 2409.20175 ↗First posted 30 Sep 2024cs.LG stat.MLcited by 18

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

Abstract (arXiv)

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. We propose Ensemble Kalman Diffusion Guidance (EnKG), a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of EnKG across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model. We open-source our code at https://github.com/devzhk/enkg-pytorch.

Key facts. Cited by 18 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 37 of its 64 references that are in the map. First posted on arXiv 30 Sep 2024.

Builds on

37 of 64 references.

Closest ancestors · 13

Same direction, newest first

  1. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  2. 2024Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpoint15 Mar
  3. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance3 Feb
  4. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  5. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
  6. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  7. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  8. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  10. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problems19 Nov
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
1 more
  1. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 24

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  5. 2023Consistency Modelscited by 1,778
  6. 2023One-step Diffusion with Distribution Matching Distillationcited by 978
  7. 2017Evolution Strategies as a Scalable Alternative to Reinforcement Learningcited by 555
  8. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  9. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Modelscited by 441
  10. 2022Fast Sampling of Diffusion Models via Operator Learningcited by 173
  11. 2024Classifier-Free Guidance is a Predictor-Correctorcited by 79
  12. 2019A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimizationcited by 66
12 more
  1. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  2. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 52
  3. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  4. 2024RB-Modulation: Training-Free Personalization of Diffusion Models using Stochastic Optimal Controlcited by 46
  5. 2018Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Taskscited by 36
  6. 2022Ensemble Kalman Methods: A Mean Field Perspectivecited by 20
  7. 2015A regularizing iterative ensemble Kalman method for PDE-constrained inverse problemscited by 13
  8. 2019Tikhonov Regularization Within Ensemble Kalman Inversioncited by 13
  9. 2024DC-Solver: Improving Predictor-Corrector Diffusion Sampler via Dynamic Compensationcited by 11
  10. 2019Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settingscited by 9
  11. 2014Deterministic Mean-field Ensemble Kalman Filteringcited by 7
  12. 2014On the Convergence of a Non-linear Ensemble Kalman Smoothercited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 9; 2026: 6.

18 papers.

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  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  2. 2025On the Guidance of Flow Matchingcited by 44
  3. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 21
  4. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  5. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  6. 2024Free2Guide: Training-Free Text-to-Video Alignment using Image LVLMcited by 9
  7. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 7
  8. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  9. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  10. 2024Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAIcited by 2
  11. 2026Training-Free Bayesian Filtering with Generative Emulatorscited by 2
  12. 2025EquiReg: Equivariance Regularized Diffusion for Inverse Problemscited by 1
6 more
  1. 2026Constrained Particle Seeking: Solving Diffusion Inverse Problems with Just Forward Passescited by 1
  2. 2026K-TRAIL: Simulator-Guided Generative Design of EM/RF Circuitscited by 1
  3. 2025Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discoverycited by 0
  4. 2026KHMP: Frequency-Domain Kalman Refinement for High-Fidelity Human Motion Predictioncited by 0
  5. 2026Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problemscited by 0
  6. 2026Aligning One-Step Generative Models with Reward-Weighted Transport Distillationcited by 0

Similar, not cited

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  2. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  3. 2024Prototype Clustered Diffusion Models for Versatile Inverse Problems
  4. 2024Diffusion State-Guided Projected Gradient for Inverse Problems
  5. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observation
  6. 2025Diffusion models for inverse problems
  7. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation
  8. 2025Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance