# GAN Prior based Null-Space Learning for Consistent Super-Resolution

arXiv: https://arxiv.org/abs/2211.13524 · HTML: https://mlsanity.com/paper/2211.13524/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 50 references that are in the map.
- First posted on arXiv 24 Nov 2022.

## Builds on (most cited first, 30 of 38)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Image2StyleGAN++: How to Edit the Embedded Images?](https://mlsanity.com/paper/1911.11544/) (2019)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Towards Real-World Blind Face Restoration with Generative Facial Prior](https://mlsanity.com/paper/2101.04061/) (2021)
- [StyleRig: Rigging StyleGAN for 3D Control over Portrait Images](https://mlsanity.com/paper/2004.00121/) (2020)
- [SEAN: Image Synthesis with Semantic Region-Adaptive Normalization](https://mlsanity.com/paper/1911.12861/) (2019)
- [GAN Prior Embedded Network for Blind Face Restoration in the Wild](https://mlsanity.com/paper/2105.06070/) (2021)
- [Image Processing Using Multi-Code GAN Prior](https://mlsanity.com/paper/1912.07116/) (2019)
- [GLEAN: Generative Latent Bank for Large-Factor Image Super-Resolution](https://mlsanity.com/paper/2012.00739/) (2020)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Bringing Old Photos Back to Life](https://mlsanity.com/paper/2004.09484/) (2020)
- [Only a Matter of Style: Age Transformation Using a Style-Based Regression Model](https://mlsanity.com/paper/2102.02754/) (2021)
- [Learning Warped Guidance for Blind Face Restoration](https://mlsanity.com/paper/1804.04829/) (2018)

## Built on by (most cited first, 22 of 22)

- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Survey on Deep Face Restoration: From Non-blind to Blind and Beyond](https://mlsanity.com/paper/2309.15490/) (2023)
- [Diffusion models for audio semantic communication](https://mlsanity.com/paper/2309.07195/) (2023)
- [Unlimited-Size Diffusion Restoration](https://mlsanity.com/paper/2303.00354/) (2023)
- [DDMM-Synth: A Denoising Diffusion Model for Cross-modal Medical Image Synthesis with Sparse-view Measurement Embedding](https://mlsanity.com/paper/2303.15770/) (2023)
- [OPDN: Omnidirectional Position-aware Deformable Network for Omnidirectional Image Super-Resolution](https://mlsanity.com/paper/2304.13471/) (2023)
- [A Trust-Guided Approach to MR Image Reconstruction with Side Information](https://mlsanity.com/paper/2501.03021/) (2025)
- [Progressive Content-aware Coded Hyperspectral Compressive Imaging](https://mlsanity.com/paper/2303.09773/) (2023)
- [Diffusion Prior Interpolation for Flexibility Real-World Face Super-Resolution](https://mlsanity.com/paper/2412.16552/) (2024)
- [NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems](https://mlsanity.com/paper/2510.01608/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [LLV-FSR: Exploiting Large Language-Vision Prior for Face Super-resolution](https://mlsanity.com/paper/2411.09293/) (2024)
- [CTSR: Controllable Fidelity-Realness Trade-off Distillation for Real-World Image Super Resolution](https://mlsanity.com/paper/2503.14272/) (2025)
- [A Range-Null Space Decomposition Approach for Fast and Flexible Spectral Compressive Imaging](https://mlsanity.com/paper/2305.09746/) (2023)
- [Detail-Enhancing Framework for Reference-Based Image Super-Resolution](https://mlsanity.com/paper/2405.00431/) (2024)
- [Equivariant Sampling for Improving Diffusion Model-based Image Restoration](https://mlsanity.com/paper/2511.09965/) (2025)
- [Random Weights Networks Work as Loss Prior Constraint for Image Restoration](https://mlsanity.com/paper/2303.16438/) (2023)
- [BARIS: Boundary-Aware Refinement with Environmental Degradation Priors for Robust Underwater Instance Segmentation](https://mlsanity.com/paper/2504.19643/) (2025)
- [LAFR: Efficient Diffusion-based Blind Face Restoration via Latent Codebook Alignment Adapter](https://mlsanity.com/paper/2505.23462/) (2025)
- [Rethinking Image Processing for the Age of AI: A Problem-First Framework for Scientific Progress](https://mlsanity.com/paper/2608.26833/) (2026)

## Abstract (arXiv)

Consistency and realness have always been the two critical issues of image super-resolution. While the realness has been dramatically improved with the use of GAN prior, the state-of-the-art methods still suffer inconsistencies in local structures and colors (e.g., tooth and eyes). In this paper, we show that these inconsistencies can be analytically eliminated by learning only the null-space component while fixing the range-space part. Further, we design a pooling-based decomposition (PD), a universal range-null space decomposition for super-resolution tasks, which is concise, fast, and parameter-free. PD can be easily applied to state-of-the-art GAN Prior based SR methods to eliminate their inconsistencies, neither compromising the realness nor bringing extra parameters or computational costs. Besides, our ablation studies reveal that PD can replace pixel-wise losses for training and achieve better generalization performance when facing unseen downsamplings or even real-world degradation. Experiments show that the use of PD refreshes state-of-the-art SR performance and speeds up the convergence of training up to 2~10 times.