# DeFlow: Learning Complex Image Degradations from Unpaired Data with Conditional Flows

arXiv: https://arxiv.org/abs/2101.05796 · HTML: https://mlsanity.com/paper/2101.05796/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 14 Jan 2021.

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

- [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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [DSLR-Quality Photos on Mobile Devices with Deep Convolutional Networks](https://mlsanity.com/paper/1704.02470/) (2017)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Frequency Separation for Real-World Super-Resolution](https://mlsanity.com/paper/1911.07850/) (2019)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [To learn image super-resolution, use a GAN to learn how to do image degradation first](https://mlsanity.com/paper/1807.11458/) (2018)
- [Unsupervised Real-world Image Super Resolution via Domain-distance Aware Training](https://mlsanity.com/paper/2004.01178/) (2020)
- [NTIRE 2020 Challenge on Real-World Image Super-Resolution: Methods and Results](https://mlsanity.com/paper/2005.01996/) (2020)
- [Unpaired Learning of Deep Image Denoising](https://mlsanity.com/paper/2008.13711/) (2020)
- [CycleGAN, a Master of Steganography](https://mlsanity.com/paper/1712.02950/) (2017)
- [Unsupervised Learning for Real-World Super-Resolution](https://mlsanity.com/paper/1909.09629/) (2019)
- [AIM 2019 Challenge on Real-World Image Super-Resolution: Methods and Results](https://mlsanity.com/paper/1911.07783/) (2019)
- [AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows](https://mlsanity.com/paper/1905.12892/) (2019)
- [Fully Unsupervised Probabilistic Noise2Void](https://mlsanity.com/paper/1911.12291/) (2019)
- [AdaFlow: Domain-Adaptive Density Estimator with Application to Anomaly Detection and Unpaired Cross-Domain Translation](https://mlsanity.com/paper/1812.05796/) (2018)

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

- [Low-Light Image Enhancement with Normalizing Flow](https://mlsanity.com/paper/2109.05923/) (2021)
- [Deep Burst Super-Resolution](https://mlsanity.com/paper/2101.10997/) (2021)
- [Multiscale Structure Guided Diffusion for Image Deblurring](https://mlsanity.com/paper/2212.01789/) (2022)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Towards Realistic Data Generation for Real-World Super-Resolution](https://mlsanity.com/paper/2406.07255/) (2024)
- [Blind Image Super-resolution with Elaborate Degradation Modeling on Noise and Kernel](https://mlsanity.com/paper/2107.00986/) (2021)
- [Towards Low Light Enhancement with RAW Images](https://mlsanity.com/paper/2112.14022/) (2021)
- [CDPMSR: Conditional Diffusion Probabilistic Models for Single Image Super-Resolution](https://mlsanity.com/paper/2302.12831/) (2023)
- [A Systematic Survey of Deep Learning-based Single-Image Super-Resolution](https://mlsanity.com/paper/2109.14335/) (2021)
- [Learn from Unpaired Data for Image Restoration: A Variational Bayes Approach](https://mlsanity.com/paper/2204.10090/) (2022)
- [ACDMSR: Accelerated Conditional Diffusion Models for Single Image Super-Resolution](https://mlsanity.com/paper/2307.00781/) (2023)
- [Noise2NoiseFlow: Realistic Camera Noise Modeling without Clean Images](https://mlsanity.com/paper/2206.01103/) (2022)
- [Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction](https://mlsanity.com/paper/2106.03135/) (2021)
- [Normalizing Flow as a Flexible Fidelity Objective for Photo-Realistic Super-resolution](https://mlsanity.com/paper/2111.03649/) (2021)
- [DaLPSR: Leverage Degradation-Aligned Language Prompt for Real-World Image Super-Resolution](https://mlsanity.com/paper/2406.16477/) (2024)
- [Learning Many-to-Many Mapping for Unpaired Real-World Image Super-resolution and Downscaling](https://mlsanity.com/paper/2310.04964/) (2023)
- [Learning Multiple Probabilistic Degradation Generators for Unsupervised Real World Image Super Resolution](https://mlsanity.com/paper/2201.10747/) (2022)
- [Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching](https://mlsanity.com/paper/2506.14605/) (2025)
- [SeNM-VAE: Semi-Supervised Noise Modeling with Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2403.17502/) (2024)
- [Self-supervision versus synthetic datasets: which is the lesser evil in the context of video denoising?](https://mlsanity.com/paper/2204.11493/) (2022)
- [NFL: Robust Learned Index via Distribution Transformation](https://mlsanity.com/paper/2205.11807/) (2022)
- [Continuous Degradation Modeling via Latent Flow Matching for Real-World Super-Resolution](https://mlsanity.com/paper/2602.04193/) (2026)
- [Enhancing Low-Light Images Using Infrared-Encoded Images](https://mlsanity.com/paper/2307.04122/) (2023)
- [Preserving Full Degradation Details for Blind Image Super-Resolution](https://mlsanity.com/paper/2407.01299/) (2024)
- [LoLiSRFlow: Joint Single Image Low-light Enhancement and Super-resolution via Cross-scale Transformer-based Conditional Flow](https://mlsanity.com/paper/2402.18871/) (2024)
- [Unsupervised Low-dose CT Reconstruction with One-way Conditional Normalizing Flows](https://mlsanity.com/paper/2410.17543/) (2024)
- [Generative Manifold Distillation: Aligning Restoration Trajectories with Natural Image Prior](https://mlsanity.com/paper/2512.11121/) (2025)
- [Unpaired Joint Distribution Modeling via Multi-Scale Image Representations](https://mlsanity.com/paper/2607.08198/) (2026)
- [sRGB Real Noise Modeling via Noise-Aware Sampling with Normalizing Flows](https://mlsanity.com/paper/2608.29038/) (2026)
- [Diffusion Based Unpaired Data Learning for Inverse Problems](https://mlsanity.com/paper/2609.01370/) (2026)

## Abstract (arXiv)

The difficulty of obtaining paired data remains a major bottleneck for learning image restoration and enhancement models for real-world applications. Current strategies aim to synthesize realistic training data by modeling noise and degradations that appear in real-world settings. We propose DeFlow, a method for learning stochastic image degradations from unpaired data. Our approach is based on a novel unpaired learning formulation for conditional normalizing flows. We model the degradation process in the latent space of a shared flow encoder-decoder network. This allows us to learn the conditional distribution of a noisy image given the clean input by solely minimizing the negative log-likelihood of the marginal distributions. We validate our DeFlow formulation on the task of joint image restoration and super-resolution. The models trained with the synthetic data generated by DeFlow outperform previous learnable approaches on three recent datasets. Code and trained models are available at: https://github.com/volflow/DeFlow