# Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning

arXiv: https://arxiv.org/abs/2409.06219 · HTML: https://mlsanity.com/paper/2409.06219/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 124 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 30 of 59)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Deep Learning on Image Denoising: An overview](https://mlsanity.com/paper/1912.13171/) (2019)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)

## Built on by (most cited first, 30 of 35)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization](https://mlsanity.com/paper/2502.03435/) (2025)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration](https://mlsanity.com/paper/2507.05604/) (2025)
- [Robust multi-coil MRI reconstruction via self-supervised denoising](https://mlsanity.com/paper/2411.12919/) (2024)
- [Localized Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2409.07968/) (2024)
- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [Transformer Meets Twicing: Harnessing Unattended Residual Information](https://mlsanity.com/paper/2503.00687/) (2025)
- [Beyond Scores: Proximal Diffusion Models](https://mlsanity.com/paper/2507.08956/) (2025)
- [Reconstruct Anything Model: a lightweight general model for computational imaging](https://mlsanity.com/paper/2503.08915/) (2025)
- [High Volume Rate 3D Ultrasound Reconstruction with Diffusion Models](https://mlsanity.com/paper/2505.22090/) (2025)
- [Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence](https://mlsanity.com/paper/2507.00719/) (2025)
- [From Linearity to Non-Linearity: How Masked Autoencoders Capture Spatial Correlations](https://mlsanity.com/paper/2508.15404/) (2025)
- [Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers](https://mlsanity.com/paper/2510.27211/) (2025)
- [Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving](https://mlsanity.com/paper/2511.06138/) (2025)
- [On the Relation Between Linear Diffusion and Power Iteration](https://mlsanity.com/paper/2410.14730/) (2024)
- [Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives](https://mlsanity.com/paper/2509.03475/) (2025)
- [Energy-Tweedie: Score meets Score, Energy meets Energy](https://mlsanity.com/paper/2512.23818/) (2025)
- [GSNR: Graph Smooth Null-Space Representation for Inverse Problems](https://mlsanity.com/paper/2602.20328/) (2026)
- [Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoising](https://mlsanity.com/paper/2603.25869/) (2026)
- [Hypothesis Testing in Imaging Inverse Problems](https://mlsanity.com/paper/2505.22481/) (2025)
- [Physics-guided denoiser network for enhanced additive manufacturing data quality](https://mlsanity.com/paper/2508.02712/) (2025)
- [Nuclear Diffusion Models for Low-Rank Background Suppression in Videos](https://mlsanity.com/paper/2509.20886/) (2025)
- [Net2Net: When Un-trained Meets Pre-trained Networks for Robust Real-World Denoising](https://mlsanity.com/paper/2510.02733/) (2025)
- [DenoGrad: A Gradient-Based Framework for Data Refinement in Tabular and Time-Series Learning](https://mlsanity.com/paper/2511.10161/) (2025)
- [Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems](https://mlsanity.com/paper/2511.12257/) (2025)
- [A low-complexity method for efficient depth-guided image deblurring](https://mlsanity.com/paper/2601.03924/) (2026)
- [Learning Affine-Equivariant Proximal Operators](https://mlsanity.com/paper/2604.15556/) (2026)
- [Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout](https://mlsanity.com/paper/2605.10008/) (2026)
- [Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study](https://mlsanity.com/paper/2606.14800/) (2026)

## Abstract (arXiv)

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in imaging, have achieved remarkable success, nearing theoretical limits by some measures. Yet, despite tens of thousands of research papers, the wide-ranging applications of denoising beyond noise removal have not been fully recognized. This is partly due to the vast and diverse literature, making a clear overview challenging. This paper aims to address this gap. We present a clarifying perspective on denoisers, their structure, and desired properties. We emphasize the increasing importance of denoising and showcase its evolution into an essential building block for complex tasks in imaging, inverse problems, and machine learning. Despite its long history, the community continues to uncover unexpected and groundbreaking uses for denoising, further solidifying its place as a cornerstone of scientific and engineering practice.