mlsanityData to 7 Oct 2026

SNaP: One-Step Posterior Sampling for Noisy Inverse Problems

arXiv 2609.34071 ↗First posted 28 Sep 2026cs.CVcited by 0

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

Abstract (arXiv)

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 × faster than iterative samplers.

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 41 of its 49 references that are in the map. First posted on arXiv 28 Sep 2026.

Builds on

41 of 49 references.

Closest ancestors · 11

Same direction, newest first

  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences14 Mar
  2. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matching3 Oct
  3. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  4. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  5. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  6. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  7. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  8. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  11. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 30

  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. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  6. 2023Consistency Modelscited by 1,778
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  8. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  9. 2025Mean Flows for One-step Generative Modelingcited by 524
  10. 2024One Step Diffusion via Shortcut Modelscited by 373
  11. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  12. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
18 more
  1. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  2. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 214
  3. 2023Denoising Diffusion Bridge Modelscited by 171
  4. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 115
  5. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  6. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 96
  7. 2023Stochastic interpolants with data-dependent couplingscited by 94
  8. 2017A Review of Convolutional Neural Networks for Inverse Problems in Imagingcited by 81
  9. 2021PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Priorcited by 78
  10. 2023Training-free Linear Image Inverses via Flowscited by 70
  11. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 65
  12. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  13. 2025Functional Mean Flow in Hilbert Spacecited by 5
  14. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generationcited by 5
  15. 2026SubFlow: Sub-mode Conditioned Flow Matching for Diverse One-Step Generationcited by 3
  16. 2026NullFlow: One-Step Generative Reconstructioncited by 2
  17. 2026MFSR: MeanFlow Distillation for One Step Real-World Image Super Resolutioncited by 1
  18. 2026Stabilizing, Scaling & Enhancing MeanFlow for Large-scale Diffusion Distillationcited by 1

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Close in wording, no citation either way

  1. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  2. 2026Posterior Continuation with Noise-Conditioned Frequency Exposure for Diffusion Inverse Problems
  3. 2024Fast Samplers for Inverse Problems in Iterative Refinement Models
  4. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  5. 2023Removing Structured Noise with Diffusion Models
  6. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM
  7. 2024Amortized Posterior Sampling with Diffusion Prior Distillation
  8. 2025Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models