# Noise Conditional Flow Model for Learning the Super-Resolution Space

arXiv: https://arxiv.org/abs/2106.04428 · HTML: https://mlsanity.com/paper/2106.04428/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 6 Jun 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (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)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [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)

## Built on by (most cited first, 19 of 19)

- [XPSR: Cross-modal Priors for Diffusion-based Image Super-Resolution](https://mlsanity.com/paper/2403.05049/) (2024)
- [CDPMSR: Conditional Diffusion Probabilistic Models for Single Image Super-Resolution](https://mlsanity.com/paper/2302.12831/) (2023)
- [Training Generative Image Super-Resolution Models by Wavelet-Domain Losses Enables Better Control of Artifacts](https://mlsanity.com/paper/2402.19215/) (2024)
- [NTIRE 2025 Challenge on Image Super-Resolution (x4): Methods and Results](https://mlsanity.com/paper/2504.14582/) (2025)
- [Generative Adversarial Networks for Image Super-Resolution: A Survey](https://mlsanity.com/paper/2204.13620/) (2022)
- [A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging](https://mlsanity.com/paper/2306.01630/) (2023)
- [Beyond Simple Edits: X-Planner for Complex Instruction-Based Image Editing](https://mlsanity.com/paper/2507.05259/) (2025)
- [FS-NCSR: Increasing Diversity of the Super-Resolution Space via Frequency Separation and Noise-Conditioned Normalizing Flow](https://mlsanity.com/paper/2204.09679/) (2022)
- [Learning Diverse Tone Styles for Image Retouching](https://mlsanity.com/paper/2207.05430/) (2022)
- [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)
- [Learning Efficient and Effective Trajectories for Differential Equation-based Image Restoration](https://mlsanity.com/paper/2410.04811/) (2024)
- [ECLARE: Efficient cross-planar learning for anisotropic resolution enhancement](https://mlsanity.com/paper/2503.11787/) (2025)
- [Dynamic-Pix2Pix: Noise Injected cGAN for Modeling Input and Target Domain Joint Distributions with Limited Training Data](https://mlsanity.com/paper/2211.08570/) (2022)
- [Harnessing the Power of Noise: A Survey of Techniques and Applications](https://mlsanity.com/paper/2410.06348/) (2024)
- [Fingerprints of Super Resolution Networks](https://mlsanity.com/paper/2410.21653/) (2024)
- [ControlMambaIR: Conditional Controls with State-Space Model for Image Restoration](https://mlsanity.com/paper/2506.02633/) (2025)
- [Revisiting the Perception-Distortion Trade-off with Spatial-Semantic Guided Super-Resolution](https://mlsanity.com/paper/2603.14112/) (2026)
- [RTE-FM-Dehazer: Radiative Transfer Equation Inspired Flow Matching for Real-World Image Dehazing](https://mlsanity.com/paper/2607.01748/) (2026)

## Abstract (arXiv)

Fundamentally, super-resolution is ill-posed problem because a low-resolution image can be obtained from many high-resolution images. Recent studies for super-resolution cannot create diverse super-resolution images. Although SRFlow tried to account for ill-posed nature of the super-resolution by predicting multiple high-resolution images given a low-resolution image, there is room to improve the diversity and visual quality. In this paper, we propose Noise Conditional flow model for Super-Resolution, NCSR, which increases the visual quality and diversity of images through noise conditional layer. To learn more diverse data distribution, we add noise to training data. However, low-quality images are resulted from adding noise. We propose the noise conditional layer to overcome this phenomenon. The noise conditional layer makes our model generate more diverse images with higher visual quality than other works. Furthermore, we show that this layer can overcome data distribution mismatch, a problem that arises in normalizing flow models. With these benefits, NCSR outperforms baseline in diversity and visual quality and achieves better visual quality than traditional GAN-based models. We also get outperformed scores at NTIRE 2021 challenge.