# CARD: Correlation Aware Restoration with Diffusion

arXiv: https://arxiv.org/abs/2512.05268 · HTML: https://mlsanity.com/paper/2512.05268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 32 of its 49 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [DiffIR: Efficient Diffusion Model for Image Restoration](https://mlsanity.com/paper/2303.09472/) (2023)
- [Deep Back-Projection Networks For Super-Resolution](https://mlsanity.com/paper/1803.02735/) (2018)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [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)
- [A Physics-based Noise Formation Model for Extreme Low-light Raw Denoising](https://mlsanity.com/paper/2003.12751/) (2020)
- [Spatially-Attentive Patch-Hierarchical Network for Adaptive Motion Deblurring](https://mlsanity.com/paper/2004.05343/) (2020)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (2022)
- [Real-world Noisy Image Denoising: A New Benchmark](https://mlsanity.com/paper/1804.02603/) (2018)
- [Physics-based Noise Modeling for Extreme Low-light Photography](https://mlsanity.com/paper/2108.02158/) (2021)
- [LG-BPN: Local and Global Blind-Patch Network for Self-Supervised Real-World Denoising](https://mlsanity.com/paper/2304.00534/) (2023)
- [Spatially Adaptive Self-Supervised Learning for Real-World Image Denoising](https://mlsanity.com/paper/2303.14934/) (2023)
- [A Review Paper: Noise Models in Digital Image Processing](https://mlsanity.com/paper/1505.03489/) (2015)

## Abstract (arXiv)

Denoising diffusion models have achieved state-of-the-art performance in image restoration by modeling the process as sequential denoising steps. However, most approaches assume independent and identically distributed (i.i.d.) Gaussian noise, while real-world sensors often exhibit spatially correlated noise due to readout mechanisms, limiting their practical effectiveness. We introduce Correlation Aware Restoration with Diffusion (CARD), a training-free extension of DDRM that explicitly handles correlated Gaussian noise. CARD first whitens the noisy observation, which converts the noise into an i.i.d. form. Then, the diffusion restoration steps are replaced with noise-whitened updates, which inherits DDRM's closed-form sampling efficiency while now being able to handle correlated noise. To emphasize the importance of addressing correlated noise, we contribute CIN-D, a novel correlated noise dataset captured across diverse illumination conditions to evaluate restoration methods on real rolling-shutter sensor noise. This dataset fills a critical gap in the literature for experimental evaluation with real-world correlated noise. Experiments on standard benchmarks with synthetic correlated noise and on CIN-D demonstrate that CARD consistently outperforms existing methods across denoising, deblurring, and super-resolution tasks.