# FS-NCSR: Increasing Diversity of the Super-Resolution Space via Frequency Separation and Noise-Conditioned Normalizing Flow

arXiv: https://arxiv.org/abs/2204.09679 · HTML: https://mlsanity.com/paper/2204.09679/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 41 references that are in the map.
- First posted on arXiv 20 Apr 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected Network](https://mlsanity.com/paper/1803.01417/) (2018)
- [ESRGAN+ : Further Improving Enhanced Super-Resolution Generative Adversarial Network](https://mlsanity.com/paper/2001.08073/) (2020)
- [Noise Conditional Flow Model for Learning the Super-Resolution Space](https://mlsanity.com/paper/2106.04428/) (2021)

## Built on by (most cited first, 8 of 8)

- [A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging](https://mlsanity.com/paper/2306.01630/) (2023)
- [NAF-DPM: A Nonlinear Activation-Free Diffusion Probabilistic Model for Document Enhancement](https://mlsanity.com/paper/2404.05669/) (2024)
- [On the Robustness of Normalizing Flows for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.04319/) (2022)
- [Boosting Flow-based Generative Super-Resolution Models via Learned Prior](https://mlsanity.com/paper/2403.10988/) (2024)
- [BlindHarmony: "Blind" Harmonization for MR Images via Flow model](https://mlsanity.com/paper/2305.10732/) (2023)
- [Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing](https://mlsanity.com/paper/2409.11738/) (2024)
- [Leveraging Vision-Language Models to Select Trustworthy Super-Resolution Samples Generated by Diffusion Models](https://mlsanity.com/paper/2506.20832/) (2025)
- [Trustworthy SR: Resolving Ambiguity in Image Super-resolution via Diffusion Models and Human Feedback](https://mlsanity.com/paper/2402.07597/) (2024)

## Abstract (arXiv)

Super-resolution suffers from an innate ill-posed problem that a single low-resolution (LR) image can be from multiple high-resolution (HR) images. Recent studies on the flow-based algorithm solve this ill-posedness by learning the super-resolution space and predicting diverse HR outputs. Unfortunately, the diversity of the super-resolution outputs is still unsatisfactory, and the outputs from the flow-based model usually suffer from undesired artifacts which causes low-quality outputs. In this paper, we propose FS-NCSR which produces diverse and high-quality super-resolution outputs using frequency separation and noise conditioning compared to the existing flow-based approaches. As the sharpness and high-quality detail of the image rely on its high-frequency information, FS-NCSR only estimates the high-frequency information of the high-resolution outputs without redundant low-frequency components. Through this, FS-NCSR significantly improves the diversity score without significant image quality degradation compared to the NCSR, the winner of the previous NTIRE 2021 challenge.