# S3Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model

arXiv: https://arxiv.org/abs/2411.11906 · HTML: https://mlsanity.com/paper/2411.11906/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Vision Mamba backbones, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 51 of its 73 references that are in the map.
- First posted on arXiv 16 Nov 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Vision Mamba backbones](https://mlsanity.com/ssm/vision-mamba-backbones/)

## Builds on (most cited first, 30 of 51)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [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)
- [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)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Activating More Pixels in Image Super-Resolution Transformer](https://mlsanity.com/paper/2205.04437/) (2022)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [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)
- [Non-Local Recurrent Network for Image Restoration](https://mlsanity.com/paper/1806.02919/) (2018)
- [Mamba-UNet: UNet-Like Pure Visual Mamba for Medical Image Segmentation](https://mlsanity.com/paper/2402.05079/) (2024)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [ChangeMamba: Remote Sensing Change Detection With Spatiotemporal State Space Model](https://mlsanity.com/paper/2404.03425/) (2024)
- [VL-Mamba: Exploring State Space Models for Multimodal Learning](https://mlsanity.com/paper/2403.13600/) (2024)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [CiaoSR: Continuous Implicit Attention-in-Attention Network for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2212.04362/) (2022)

## Built on by (most cited first, 12 of 12)

- [Pixel to Gaussian: Ultra-Fast Continuous Super-Resolution with 2D Gaussian Modeling](https://mlsanity.com/paper/2503.06617/) (2025)
- [Depth-Synergized Mamba Meets Memory Experts for All-Day Image Reflection Separation](https://mlsanity.com/paper/2601.00322/) (2026)
- [Diffusion-Based Image Editing: An Unforeseen Adversary to Robust Invisible Watermarks](https://mlsanity.com/paper/2511.05598/) (2025)
- [SSCM: A Spatial-Semantic Consistent Model for Multi-Contrast MRI Super-Resolution](https://mlsanity.com/paper/2509.18593/) (2025)
- [Vanishing Watermarks: Diffusion-Based Image Editing Undermines Robust Invisible Watermarking](https://mlsanity.com/paper/2602.20680/) (2026)
- [Editing on the Generative Manifold: A Theoretical and Empirical Study of General Diffusion-Based Image Editing Trade-offs](https://mlsanity.com/paper/2603.29736/) (2026)
- [SemaMIL: Semantic-Aware Multiple Instance Learning with Retrieval-Guided State Space Modeling for Whole Slide Images](https://mlsanity.com/paper/2509.00442/) (2025)
- [DeRainMamba: A Frequency-Aware State Space Model with Detail Enhancement for Image Deraining](https://mlsanity.com/paper/2510.06746/) (2025)
- [When Denoising Becomes Unsigning: Theoretical and Empirical Analysis of Watermark Fragility Under Diffusion-Based Image Editing](https://mlsanity.com/paper/2603.04696/) (2026)
- [Editing Away the Evidence: Diffusion-Based Image Manipulation and the Failure Modes of Robust Watermarking](https://mlsanity.com/paper/2603.12949/) (2026)
- [ReconMIL: Synergizing Latent Space Reconstruction with Bi-Stream Mamba for Whole Slide Image Analysis](https://mlsanity.com/paper/2603.19925/) (2026)
- [Interactive State Space Model with Cross-Modal Local Scanning for Depth Super-Resolution](https://mlsanity.com/paper/2605.11934/) (2026)

## Abstract (arXiv)

Arbitrary scale super-resolution (ASSR) aims to super-resolve low-resolution images to high-resolution images at any scale using a single model, addressing the limitations of traditional super-resolution methods that are restricted to fixed-scale factors (e.g., ×2, ×4). The advent of Implicit Neural Representations (INR) has brought forth a plethora of novel methodologies for ASSR, which facilitate the reconstruction of original continuous signals by modeling a continuous representation space for coordinates and pixel values, thereby enabling arbitrary-scale super-resolution. Consequently, the primary objective of ASSR is to construct a continuous representation space derived from low-resolution inputs. However, existing methods, primarily based on CNNs and Transformers, face significant challenges such as high computational complexity and inadequate modeling of long-range dependencies, which hinder their effectiveness in real-world applications. To overcome these limitations, we propose a novel arbitrary-scale super-resolution method, called S3Mamba, to construct a scalable continuous representation space. Specifically, we propose a Scalable State Space Model (SSSM) to modulate the state transition matrix and the sampling matrix of step size during the discretization process, achieving scalable and continuous representation modeling with linear computational complexity. Additionally, we propose a novel scale-aware self-attention mechanism to further enhance the network's ability to perceive global important features at different scales, thereby building the S3Mamba to achieve superior arbitrary-scale super-resolution. Extensive experiments on both synthetic and real-world benchmarks demonstrate that our method achieves state-of-the-art performance and superior generalization capabilities at arbitrary super-resolution scales.