# SVNR: Spatially-variant Noise Removal with Denoising Diffusion arXiv: https://arxiv.org/abs/2306.16052 ยท HTML: https://mlsanity.com/paper/2306.16052/ ## Key facts - Cited by 8 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 32 of its 40 references that are in the map. - First posted on arXiv 28 Jun 2023. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 32) - [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) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022) - [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022) - [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016) - [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021) - [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022) - [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021) - [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022) - [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017) - [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018) - [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017) - [Learning to See in the Dark](https://mlsanity.com/paper/1805.01934/) (2018) - [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019) - [Unprocessing Images for Learned Raw Denoising](https://mlsanity.com/paper/1811.11127/) (2018) - [HINet: Half Instance Normalization Network for Image Restoration](https://mlsanity.com/paper/2105.06086/) (2021) - [Benchmarking Denoising Algorithms with Real Photographs](https://mlsanity.com/paper/1707.01313/) (2017) - [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021) - [Burst Denoising with Kernel Prediction Networks](https://mlsanity.com/paper/1712.02327/) (2017) - [A Physics-based Noise Formation Model for Extreme Low-light Raw Denoising](https://mlsanity.com/paper/2003.12751/) (2020) - [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019) - [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023) - [Spatial-Adaptive Network for Single Image Denoising](https://mlsanity.com/paper/2001.10291/) (2020) - [NAN: Noise-Aware NeRFs for Burst-Denoising](https://mlsanity.com/paper/2204.04668/) (2022) - [Dancing under the stars: video denoising in starlight](https://mlsanity.com/paper/2204.04210/) (2022) - [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021) - [RENOIR - A Dataset for Real Low-Light Image Noise Reduction](https://mlsanity.com/paper/1409.8230/) (2014) - [IDR: Self-Supervised Image Denoising via Iterative Data Refinement](https://mlsanity.com/paper/2111.14358/) (2021) ## Built on by (most cited first, 8 of 8) - [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023) - [Time-to-Move: Training-Free Motion Controlled Video Generation via Dual-Clock Denoising](https://mlsanity.com/paper/2511.08633/) (2025) - [PFCM: Poisson flow consistency models for low-dose CT image denoising](https://mlsanity.com/paper/2402.08159/) (2024) - [Tell Me What You See: Text-Guided Real-World Image Denoising](https://mlsanity.com/paper/2312.10191/) (2023) - [DifuzCam: Replacing Camera Lens with a Mask and a Diffusion Model](https://mlsanity.com/paper/2408.07541/) (2024) - [Perception-based multiplicative noise removal using SDEs](https://mlsanity.com/paper/2408.10283/) (2024) - [Denoising Diffusion as a New Framework for Underwater Images](https://mlsanity.com/paper/2510.09934/) (2025) - [Region-Adaptive Generative Compression with Spatially Varying Diffusion Models](https://mlsanity.com/paper/2604.01122/) (2026) ## Abstract (arXiv) Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.