# Normalizing Flow as a Flexible Fidelity Objective for Photo-Realistic Super-resolution

arXiv: https://arxiv.org/abs/2111.03649 · HTML: https://mlsanity.com/paper/2111.03649/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 5 Nov 2021.

## Builds on (most cited first, 30 of 33)

- [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)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [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)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Deep multi-scale video prediction beyond mean square error](https://mlsanity.com/paper/1511.05440/) (2015)
- [Deep Back-Projection Networks For Super-Resolution](https://mlsanity.com/paper/1803.02735/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [EnhanceNet: Single Image Super-Resolution Through Automated Texture Synthesis](https://mlsanity.com/paper/1612.07919/) (2016)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [The 2018 PIRM Challenge on Perceptual Image Super-resolution](https://mlsanity.com/paper/1809.07517/) (2018)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [RankSRGAN: Generative Adversarial Networks with Ranker for Image Super-Resolution](https://mlsanity.com/paper/1908.06382/) (2019)
- [Frequency Separation for Real-World Super-Resolution](https://mlsanity.com/paper/1911.07850/) (2019)
- [Invertible Image Rescaling](https://mlsanity.com/paper/2005.05650/) (2020)
- [NTIRE 2020 Challenge on Real-World Image Super-Resolution: Methods and Results](https://mlsanity.com/paper/2005.01996/) (2020)
- [Progressive Face Super-Resolution via Attention to Facial Landmark](https://mlsanity.com/paper/1908.08239/) (2019)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Unsupervised Learning for Real-World Super-Resolution](https://mlsanity.com/paper/1909.09629/) (2019)
- [C-Flow: Conditional Generative Flow Models for Images and 3D Point Clouds](https://mlsanity.com/paper/1912.07009/) (2019)

## Built on by (most cited first, 10 of 10)

- [Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2303.05156/) (2023)
- [Collapse by Conditioning: Training Class-conditional GANs with Limited Data](https://mlsanity.com/paper/2201.06578/) (2022)
- [Reversing Flow for Image Restoration](https://mlsanity.com/paper/2506.16961/) (2025)
- [On the Robustness of Normalizing Flows for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.04319/) (2022)
- [Learning Many-to-Many Mapping for Unpaired Real-World Image Super-resolution and Downscaling](https://mlsanity.com/paper/2310.04964/) (2023)
- [Boosting Flow-based Generative Super-Resolution Models via Learned Prior](https://mlsanity.com/paper/2403.10988/) (2024)
- [Invertible Monotone Operators for Normalizing Flows](https://mlsanity.com/paper/2210.08176/) (2022)
- [Self-Adaptive Reality-Guided Diffusion for Artifact-Free Super-Resolution](https://mlsanity.com/paper/2403.16643/) (2024)
- [Towards Climate Variable Prediction with Conditioned Spatio-Temporal Normalizing Flows](https://mlsanity.com/paper/2311.06958/) (2023)
- [A General Method to Incorporate Spatial Information into Loss Functions for GAN-based Super-resolution Models](https://mlsanity.com/paper/2403.10589/) (2024)

## Abstract (arXiv)

Super-resolution is an ill-posed problem, where a ground-truth high-resolution image represents only one possibility in the space of plausible solutions. Yet, the dominant paradigm is to employ pixel-wise losses, such as L_1, which drive the prediction towards a blurry average. This leads to fundamentally conflicting objectives when combined with adversarial losses, which degrades the final quality. We address this issue by revisiting the L_1 loss and show that it corresponds to a one-layer conditional flow. Inspired by this relation, we explore general flows as a fidelity-based alternative to the L_1 objective. We demonstrate that the flexibility of deeper flows leads to better visual quality and consistency when combined with adversarial losses. We conduct extensive user studies for three datasets and scale factors, where our approach is shown to outperform state-of-the-art methods for photo-realistic super-resolution. Code and trained models will be available at: git.io/AdFlow