mlsanityData to 7 Oct 2026

Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping

arXiv 2605.27990 ↗First posted 27 May 2026cs.LG cs.AI cs.CVcited by 0

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

Abstract (arXiv)

Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates. The correction pulls likelihood gradients back through the denoiser, uses a one-sided curvature model that avoids forward denoiser Jacobians, and applies diffusion-calibrated rank-one damping aligned with the denoiser residual. Each correction is solved with matrix-free GMRES using automatic differentiation, and sampling proceeds with a variance-preserving Langevin transition with a closed-form drift/noise split. On FFHQ and ImageNet across inverse problems, it achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines; on accelerated MRI reconstruction, it achieves the best PSNR/SSIM among the compared baselines.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 30 of its 48 references that are in the map. First posted on arXiv 27 May 2026.

Builds on

30 of 48 references.

Closest ancestors · 13

Same direction, newest first

  1. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems6 Oct
  2. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling13 Sep
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  4. 2024DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models27 May
  5. 2023Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance27 Dec
  6. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  7. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  8. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  9. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  10. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  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 · 17

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  4. 2020Denoising Diffusion Implicit Modelscited by 9,655
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  9. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  11. 2015Automatic differentiation in machine learning: a surveycited by 846
  12. 2019On the Variance of the Adaptive Learning Rate and Beyondcited by 763
5 more
  1. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  2. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  3. 2021Early Stopping for Deep Image Priorcited by 44
  4. 2024Fast constrained sampling in pre-trained diffusion modelscited by 9
  5. 2025Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Samplingcited by 2

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  1. 2026Geometry-Aware Diffusion Guidance via Curvature-Adaptive Tubular Correction
  2. 2026Posterior Continuation with Noise-Conditioned Frequency Exposure for Diffusion Inverse Problems
  3. 2026A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
  4. 2025SURE Guided Posterior Sampling: Trajectory Correction for Diffusion-Based Inverse Problems
  5. 2026Sparse Scheduled Diffusion Guidance for Inverse Problems
  6. 2025Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm
  7. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  8. 2026Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps