# SRFlow: Learning the Super-Resolution Space with Normalizing Flow

arXiv: https://arxiv.org/abs/2006.14200 · HTML: https://mlsanity.com/paper/2006.14200/

## Key facts

- Cited by 209 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 30 of 209)

- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Scaling Up to Excellence: Practicing Model Scaling for Photo-Realistic Image Restoration In the Wild](https://mlsanity.com/paper/2401.13627/) (2024)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [SinSR: Diffusion-Based Image Super-Resolution in a Single Step](https://mlsanity.com/paper/2311.14760/) (2023)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Low-Light Image Enhancement with Normalizing Flow](https://mlsanity.com/paper/2109.05923/) (2021)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Enhanced Invertible Encoding for Learned Image Compression](https://mlsanity.com/paper/2108.03690/) (2021)
- [ShadowDiffusion: When Degradation Prior Meets Diffusion Model for Shadow Removal](https://mlsanity.com/paper/2212.04711/) (2022)
- [Deep Burst Super-Resolution](https://mlsanity.com/paper/2101.10997/) (2021)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Flow-based Kernel Prior with Application to Blind Super-Resolution](https://mlsanity.com/paper/2103.15977/) (2021)
- [Fourier Space Losses for Efficient Perceptual Image Super-Resolution](https://mlsanity.com/paper/2106.00783/) (2021)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Efficient Diffusion Model for Image Restoration by Residual Shifting](https://mlsanity.com/paper/2403.07319/) (2024)
- [Towards Blind Watermarking: Combining Invertible and Non-invertible Mechanisms](https://mlsanity.com/paper/2212.12678/) (2022)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [Towards Realistic Data Generation for Real-World Super-Resolution](https://mlsanity.com/paper/2406.07255/) (2024)
- [ResDiff: Combining CNN and Diffusion Model for Image Super-Resolution](https://mlsanity.com/paper/2303.08714/) (2023)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Stochastic Image-to-Video Synthesis using cINNs](https://mlsanity.com/paper/2105.04551/) (2021)
- [Deep Constrained Least Squares for Blind Image Super-Resolution](https://mlsanity.com/paper/2202.07508/) (2022)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Deep Learning-based Image and Video Inpainting: A Survey](https://mlsanity.com/paper/2401.03395/) (2024)
- [iPOKE: Poking a Still Image for Controlled Stochastic Video Synthesis](https://mlsanity.com/paper/2107.02790/) (2021)
- [Do better ImageNet classifiers assess perceptual similarity better?](https://mlsanity.com/paper/2203.04946/) (2022)

## Abstract (arXiv)

Super-resolution is an ill-posed problem, since it allows for multiple predictions for a given low-resolution image. This fundamental fact is largely ignored by state-of-the-art deep learning based approaches. These methods instead train a deterministic mapping using combinations of reconstruction and adversarial losses. In this work, we therefore propose SRFlow: a normalizing flow based super-resolution method capable of learning the conditional distribution of the output given the low-resolution input. Our model is trained in a principled manner using a single loss, namely the negative log-likelihood. SRFlow therefore directly accounts for the ill-posed nature of the problem, and learns to predict diverse photo-realistic high-resolution images. Moreover, we utilize the strong image posterior learned by SRFlow to design flexible image manipulation techniques, capable of enhancing super-resolved images by, e.g., transferring content from other images. We perform extensive experiments on faces, as well as on super-resolution in general. SRFlow outperforms state-of-the-art GAN-based approaches in terms of both PSNR and perceptual quality metrics, while allowing for diversity through the exploration of the space of super-resolved solutions.