# CUF: Continuous Upsampling Filters

arXiv: https://arxiv.org/abs/2210.06965 · HTML: https://mlsanity.com/paper/2210.06965/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [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)
- [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)
- [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)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [A Deep Journey into Super-resolution: A survey](https://mlsanity.com/paper/1904.07523/) (2019)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [ConvPoint: Continuous Convolutions for Point Cloud Processing](https://mlsanity.com/paper/1904.02375/) (2019)
- [Real-Time Quantized Image Super-Resolution on Mobile NPUs, Mobile AI 2021 Challenge: Report](https://mlsanity.com/paper/2105.07825/) (2021)
- [Anchor-based Plain Net for Mobile Image Super-Resolution](https://mlsanity.com/paper/2105.09750/) (2021)
- [A Comprehensive Review of Deep Learning-based Single Image Super-resolution](https://mlsanity.com/paper/2102.09351/) (2021)

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

- [Neural Field Convolutions by Repeated Differentiation](https://mlsanity.com/paper/2304.01834/) (2023)
- [Arbitrary-Scale Video Super-Resolution with Structural and Textural Priors](https://mlsanity.com/paper/2407.09919/) (2024)
- [SMPConv: Self-moving Point Representations for Continuous Convolution](https://mlsanity.com/paper/2304.02330/) (2023)
- [Thera: Aliasing-Free Arbitrary-Scale Super-Resolution with Neural Heat Fields](https://mlsanity.com/paper/2311.17643/) (2023)
- [Learnable Fractional Reaction-Diffusion Dynamics for Under-Display ToF Imaging and Beyond](https://mlsanity.com/paper/2511.01704/) (2025)
- [Arbitrary-Scale Downscaling of Tidal Current Data Using Implicit Continuous Representation](https://mlsanity.com/paper/2401.15893/) (2024)
- [Super-Resolving Unseen Hyperspectral Sensors at Any Scale via Spatial Operators](https://mlsanity.com/paper/2609.39926/) (2026)
- [Any-scale Object Detection using Arbitrary-scaled Images](https://mlsanity.com/paper/2610.04346/) (2026)

## Abstract (arXiv)

Neural fields have rapidly been adopted for representing 3D signals, but their application to more classical 2D image-processing has been relatively limited. In this paper, we consider one of the most important operations in image processing: upsampling. In deep learning, learnable upsampling layers have extensively been used for single image super-resolution. We propose to parameterize upsampling kernels as neural fields. This parameterization leads to a compact architecture that obtains a 40-fold reduction in the number of parameters when compared with competing arbitrary-scale super-resolution architectures. When upsampling images of size 256x256 we show that our architecture is 2x-10x more efficient than competing arbitrary-scale super-resolution architectures, and more efficient than sub-pixel convolutions when instantiated to a single-scale model. In the general setting, these gains grow polynomially with the square of the target scale. We validate our method on standard benchmarks showing such efficiency gains can be achieved without sacrifices in super-resolution performance.