# MB-TaylorFormer V2: Improved Multi-branch Linear Transformer Expanded by Taylor Formula for Image Restoration

arXiv: https://arxiv.org/abs/2501.04486 · HTML: https://mlsanity.com/paper/2501.04486/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 104 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 30 of 62)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [CSWin Transformer: A General Vision Transformer Backbone with Cross-Shaped Windows](https://mlsanity.com/paper/2107.00652/) (2021)
- [MaxViT: Multi-Axis Vision Transformer](https://mlsanity.com/paper/2204.01697/) (2022)
- [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [Rethinking Coarse-to-Fine Approach in Single Image Deblurring](https://mlsanity.com/paper/2108.05054/) (2021)
- [Learning Enriched Features for Real Image Restoration and Enhancement](https://mlsanity.com/paper/2003.06792/) (2020)
- [FFA-Net: Feature Fusion Attention Network for Single Image Dehazing](https://mlsanity.com/paper/1911.07559/) (2019)
- [MAXIM: Multi-Axis MLP for Image Processing](https://mlsanity.com/paper/2201.02973/) (2022)
- [Progressive Image Deraining Networks: A Better and Simpler Baseline](https://mlsanity.com/paper/1901.09221/) (2019)
- [Multi-Scale Progressive Fusion Network for Single Image Deraining](https://mlsanity.com/paper/2003.10985/) (2020)
- [DiffIR: Efficient Diffusion Model for Image Restoration](https://mlsanity.com/paper/2303.09472/) (2023)

## Built on by (most cited first, 30 of 36)

- [Gradient as Conditions: Rethinking HOG for All-in-one Image Restoration](https://mlsanity.com/paper/2504.09377/) (2025)
- [DSwinIR: Rethinking Window-based Attention for Image Restoration](https://mlsanity.com/paper/2504.04869/) (2025)
- [M2Restore: Mixture-of-Experts-based Mamba-CNN Fusion Framework for All-in-One Image Restoration](https://mlsanity.com/paper/2506.07814/) (2025)
- [From Zero to Detail: A Progressive Spectral Decoupling Paradigm for UHD Image Restoration with New Benchmark](https://mlsanity.com/paper/2604.15654/) (2026)
- [LIFT: A Novel Framework for Enhancing Long-Context Understanding of LLMs via Long Input Fine-Tuning](https://mlsanity.com/paper/2502.14644/) (2025)
- [DPMambaIR: All-in-One Image Restoration via Degradation-Aware Prompt State Space Model](https://mlsanity.com/paper/2504.17732/) (2025)
- [UDPNet: Unleashing Depth-based Priors for Robust Image Dehazing](https://mlsanity.com/paper/2601.06909/) (2026)
- [Efficient Dual-domain Image Dehazing with Haze Prior Perception](https://mlsanity.com/paper/2507.11035/) (2025)
- [Fourier-RWKV: A Multi-State Perception Network for Efficient Image Dehazing](https://mlsanity.com/paper/2512.08161/) (2025)
- [All-in-One Image Restoration via Causal-Deconfounding Wavelet-Disentangled Prompt Network](https://mlsanity.com/paper/2603.03839/) (2026)
- [Task-Guided Prompting for Unified Remote Sensing Image Restoration](https://mlsanity.com/paper/2604.02742/) (2026)
- [CoRE-UIR: Prior-guided common and residual experts for efficient all-in-one remote sensing image restoration](https://mlsanity.com/paper/2607.27898/) (2026)
- [WDMamba: When Wavelet Degradation Prior Meets Vision Mamba for Image Dehazing](https://mlsanity.com/paper/2505.04369/) (2025)
- [MoCHA-former: Moir'e-Conditioned Hybrid Adaptive Transformer for Video Demoir'eing](https://mlsanity.com/paper/2508.14423/) (2025)
- [HiRQA: Hierarchical Ranking and Quality Alignment for Opinion-Unaware Image Quality Assessment](https://mlsanity.com/paper/2508.15130/) (2025)
- [Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection](https://mlsanity.com/paper/2509.07654/) (2025)
- [Clear Roads, Clear Vision: Advancements in Multi-Weather Restoration for Smart Transportation](https://mlsanity.com/paper/2510.09228/) (2025)
- [Efficient Vision Mamba for MRI Super-Resolution via Hybrid Selective Scanning](https://mlsanity.com/paper/2512.19676/) (2025)
- [ATT-CR: Adaptive Triangular Transformer for Cloud Removal](https://mlsanity.com/paper/2606.05999/) (2026)
- [Multi-Knowledge-oriented Nighttime Haze Imaging Enhancer for Vision-driven Intelligent Systems](https://mlsanity.com/paper/2502.07351/) (2025)
- [Photovoltaic Defect Image Generator with Boundary Alignment Smoothing Constraint for Domain Shift Mitigation](https://mlsanity.com/paper/2505.06117/) (2025)
- [FOCUS: Frequency-Optimized Conditioning of DiffUSion Models for mitigating catastrophic forgetting during Test-Time Adaptation](https://mlsanity.com/paper/2508.14437/) (2025)
- [Defense against Unauthorized Distillation in Image Restoration via Feature Space Perturbation](https://mlsanity.com/paper/2510.08925/) (2025)
- [LightQANet: Quantized and Adaptive Feature Learning for Low-Light Image Enhancement](https://mlsanity.com/paper/2510.14753/) (2025)
- [SemanticStitch: Enhancing Image Coherence through Foreground-Aware Seam Carving](https://mlsanity.com/paper/2511.12084/) (2025)
- [ZID-Net: Zero-Inference Diffusion Prior Decoupling Network for Single Image Dehazing](https://mlsanity.com/paper/2604.23709/) (2026)
- [Beyond Fidelity: Semantic Similarity Assessment in Low-Level Image Processing](https://mlsanity.com/paper/2604.25408/) (2026)
- [MARR: Module-Adaptive Residual Reconstruction for Low-Bit Post-Training Quantization](https://mlsanity.com/paper/2605.17997/) (2026)
- [EvoIR-Agent: Self-Evolving Image Restoration Agentic System via Experience-Driven Learning](https://mlsanity.com/paper/2605.22208/) (2026)
- [DVANet: Degradation-aware Visual-prior Alignment Network for Image Restoration](https://mlsanity.com/paper/2606.19097/) (2026)

## Abstract (arXiv)

Recently, Transformer networks have demonstrated outstanding performance in the field of image restoration due to the global receptive field and adaptability to input. However, the quadratic computational complexity of Softmax-attention poses a significant limitation on its extensive application in image restoration tasks, particularly for high-resolution images. To tackle this challenge, we propose a novel variant of the Transformer. This variant leverages the Taylor expansion to approximate the Softmax-attention and utilizes the concept of norm-preserving mapping to approximate the remainder of the first-order Taylor expansion, resulting in a linear computational complexity. Moreover, we introduce a multi-branch architecture featuring multi-scale patch embedding into the proposed Transformer, which has four distinct advantages: 1) various sizes of the receptive field; 2) multi-level semantic information; 3) flexible shapes of the receptive field; 4) accelerated training and inference speed. Hence, the proposed model, named the second version of Taylor formula expansion-based Transformer (for short MB-TaylorFormer V2) has the capability to concurrently process coarse-to-fine features, capture long-distance pixel interactions with limited computational cost, and improve the approximation of the Taylor expansion remainder. Experimental results across diverse image restoration benchmarks demonstrate that MB-TaylorFormer V2 achieves state-of-the-art performance in multiple image restoration tasks, such as image dehazing, deraining, desnowing, motion deblurring, and denoising, with very little computational overhead. The source code is available at https://github.com/FVL2020/MB-TaylorFormerV2.