# Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolution

arXiv: https://arxiv.org/abs/2303.05156 · HTML: https://mlsanity.com/paper/2303.05156/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 50 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 30 of 38)

- [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)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [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 via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (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)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform](https://mlsanity.com/paper/1804.02815/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [RankSRGAN: Generative Adversarial Networks with Ranker for Image Super-Resolution](https://mlsanity.com/paper/1908.06382/) (2019)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)

## Built on by (most cited first, 30 of 34)

- [DiSR-NeRF: Diffusion-Guided View-Consistent Super-Resolution NeRF](https://mlsanity.com/paper/2404.00874/) (2024)
- [Reversible Decoupling Network for Single Image Reflection Removal](https://mlsanity.com/paper/2410.08063/) (2024)
- [Latent Modulated Function for Computational Optimal Continuous Image Representation](https://mlsanity.com/paper/2404.16451/) (2024)
- [Generalized and Efficient 2D Gaussian Splatting for Arbitrary-scale Super-Resolution](https://mlsanity.com/paper/2501.06838/) (2025)
- [HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution](https://mlsanity.com/paper/2412.03748/) (2024)
- [Residual-Conditioned Optimal Transport: Towards Structure-Preserving Unpaired and Paired Image Restoration](https://mlsanity.com/paper/2405.02843/) (2024)
- [S3Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model](https://mlsanity.com/paper/2411.11906/) (2024)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [HoliSDiP: Image Super-Resolution via Holistic Semantics and Diffusion Prior](https://mlsanity.com/paper/2411.18662/) (2024)
- [Boosting Flow-based Generative Super-Resolution Models via Learned Prior](https://mlsanity.com/paper/2403.10988/) (2024)
- [DEAL: Data-Efficient Adversarial Learning for High-Quality Infrared Imaging](https://mlsanity.com/paper/2503.00905/) (2025)
- [Augmenting Perceptual Super-Resolution via Image Quality Predictors](https://mlsanity.com/paper/2504.18524/) (2025)
- [HR-INR: Continuous Space-Time Video Super-Resolution via Event Camera](https://mlsanity.com/paper/2405.13389/) (2024)
- [Hallucination Score: Towards Mitigating Hallucinations in Generative Image Super-Resolution](https://mlsanity.com/paper/2507.14367/) (2025)
- [Training-Free Model Ensemble for Single-Image Super-Resolution via Strong-Branch Compensation](https://mlsanity.com/paper/2604.11564/) (2026)
- [Rotation Equivariant Arbitrary-scale Image Super-Resolution](https://mlsanity.com/paper/2508.05160/) (2025)
- [SR-CACO-2: A Dataset for Confocal Fluorescence Microscopy Image Super-Resolution](https://mlsanity.com/paper/2406.09168/) (2024)
- [ASSR-NeRF: Arbitrary-Scale Super-Resolution on Voxel Grid for High-Quality Radiance Fields Reconstruction](https://mlsanity.com/paper/2406.20066/) (2024)
- [LeRF: Learning Resampling Function for Adaptive and Efficient Image Interpolation](https://mlsanity.com/paper/2407.09935/) (2024)
- [Multiscale Corrections by Continuous Super-Resolution](https://mlsanity.com/paper/2411.07576/) (2024)
- [Your Super Resolution Model is not Enough for Tackling Real-World Scenarios](https://mlsanity.com/paper/2509.06387/) (2025)
- [Deep Learning Empowered Super-Resolution: A Comprehensive Survey and Future Prospects](https://mlsanity.com/paper/2509.22692/) (2025)
- [CDFlow: Building Invertible Layers with Circulant and Diagonal Matrices](https://mlsanity.com/paper/2510.25323/) (2025)
- [CASR: A Robust Cyclic Framework for Arbitrary Large-Scale Super-Resolution with Distribution Alignment and Self-Similarity Awareness](https://mlsanity.com/paper/2602.22159/) (2026)
- [Calibrated Multivariate Regression with Localized PIT Mappings](https://mlsanity.com/paper/2409.10855/) (2024)
- [Towards Arbitrary-Scale Spacecraft Image Super-Resolution via Salient Region-Guidance](https://mlsanity.com/paper/2504.18127/) (2025)
- [Stroke-based Cyclic Amplifier: Image Super-Resolution at Arbitrary Ultra-Large Scales](https://mlsanity.com/paper/2506.10774/) (2025)
- [Implicit Neural Representation-Based Continuous Single Image Super-Resolution: An Empirical Benchmark](https://mlsanity.com/paper/2601.17723/) (2026)
- [Perceptual Quality Optimization of Image Super-Resolution](https://mlsanity.com/paper/2602.21482/) (2026)
- [Fidelity- and Perception-Aware Local Implicit Attention for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2606.21910/) (2026)

## Abstract (arXiv)

Flow-based methods have demonstrated promising results in addressing the ill-posed nature of super-resolution (SR) by learning the distribution of high-resolution (HR) images with the normalizing flow. However, these methods can only perform a predefined fixed-scale SR, limiting their potential in real-world applications. Meanwhile, arbitrary-scale SR has gained more attention and achieved great progress. Nonetheless, previous arbitrary-scale SR methods ignore the ill-posed problem and train the model with per-pixel L1 loss, leading to blurry SR outputs. In this work, we propose "Local Implicit Normalizing Flow" (LINF) as a unified solution to the above problems. LINF models the distribution of texture details under different scaling factors with normalizing flow. Thus, LINF can generate photo-realistic HR images with rich texture details in arbitrary scale factors. We evaluate LINF with extensive experiments and show that LINF achieves the state-of-the-art perceptual quality compared with prior arbitrary-scale SR methods.