mlsanityData to 7 Oct 2026

Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models

arXiv 2510.23633 ↗First posted 24 Oct 2025cs.LG cs.AI cs.CVcited by 2

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

Abstract (arXiv)

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma: excessive integration can disrupt the generative process, while insufficient integration fails to emphasize the constraints imposed by the inverse problem. To address this, we propose Noise Combination Sampling, a novel method that synthesizes an optimal noise vector from a noise subspace to approximate the measurement score, replacing the noise term in the standard Denoising Diffusion Probabilistic Models process. This enables conditional information to be naturally embedded into the generation process without reliance on step-wise hyperparameter tuning. Our method can be applied to a wide range of inverse problem solvers, including image compression, and, particularly when the number of generation steps T is small, achieves superior performance with negligible computational overhead, significantly improving robustness and stability.

Key facts. Cited by 2 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 31 of its 42 references that are in the map. First posted on arXiv 24 Oct 2025.

Builds on

31 of 42 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences14 Mar
  2. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  4. 2023Regularization by Texts for Latent Diffusion Inverse Solvers27 Nov
  5. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  6. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  7. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2022Classifier-Free Diffusion Guidancecited by 5,717
  7. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  8. 2022Video Diffusion Modelscited by 2,280
  9. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  10. 2025Large Language Diffusion Modelscited by 872
  11. 2020High-Fidelity Generative Image Compressioncited by 331
  12. 2023Your Diffusion Model is Secretly a Zero-Shot Classifiercited by 301
11 more
  1. 2024Discrete Flow Matchingcited by 301
  2. 2023DragDiffusion: Harnessing Diffusion Models for Interactive Point-based Image Editingcited by 293
  3. 2023FreeDoM: Training-Free Energy-Guided Conditional Diffusion Modelcited by 290
  4. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  5. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  6. 2023Manifold Preserving Guided Diffusioncited by 153
  7. 2023Diffuse, Attend, and Segment: Unsupervised Zero-Shot Segmentation using Stable Diffusioncited by 131
  8. 2024TFG: Unified Training-Free Guidance for Diffusion Modelscited by 103
  9. 2023Improving Statistical Fidelity for Neural Image Compression with Implicit Local Likelihood Modelscited by 90
  10. 2024Guidance with Spherical Gaussian Constraint for Conditional Diffusioncited by 69
  11. 2025Compressed Image Generation with Denoising Diffusion Codebook Modelscited by 24

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Turbo-DDCM: Fast and Flexible Zero-Shot Diffusion-Based Image Compressioncited by 4
  2. 2026GVCC: Zero-Shot Video Compression via Codebook-Driven Stochastic Rectified Flowcited by 2

Similar, not cited

Close in wording, no citation either way

  1. 2025Zero-Shot Solving of Imaging Inverse Problems via Noise-Refined Likelihood Guided Diffusion Models
  2. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
  3. 2026Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  5. 2023Removing Structured Noise with Diffusion Models
  6. 2025Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance
  7. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  8. 2025Diffusion models for inverse problems