# Learning Adaptive Dynamical Features via Multi-τ Liquid-Mamba for All-in-one Image Restoration arXiv: https://arxiv.org/abs/2606.22801 · HTML: https://mlsanity.com/paper/2606.22801/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Placed in Mamba for image restoration, one of 10 directions in State-space sequence models (S4, Mamba). - Builds on 44 of its 78 references that are in the map. - First posted on arXiv 22 Jun 2026. ## Placed in - State-space sequence models (S4, Mamba) / [Mamba for image restoration](https://mlsanity.com/ssm/mamba-for-image-restoration/) ## Builds on (most cited first, 30 of 44) - [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) - [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016) - [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017) - [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024) - [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021) - [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022) - [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) - [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021) - [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017) - [NIMA: Neural Image Assessment](https://mlsanity.com/paper/1709.05424/) (2017) - [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016) - [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024) - [Density-aware Single Image De-raining using a Multi-stream Dense Network](https://mlsanity.com/paper/1802.07412/) (2018) - [DesnowNet: Context-Aware Deep Network for Snow Removal](https://mlsanity.com/paper/1708.04512/) (2017) - [Image De-raining Using a Conditional Generative Adversarial Network](https://mlsanity.com/paper/1701.05957/) (2017) - [Human-Aware Motion Deblurring](https://mlsanity.com/paper/2001.06816/) (2020) - [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020) - [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022) - [PromptIR: Prompting for All-in-One Blind Image Restoration](https://mlsanity.com/paper/2306.13090/) (2023) - [AdaIR: Adaptive All-in-One Image Restoration via Frequency Mining and Modulation](https://mlsanity.com/paper/2403.14614/) (2024) - [AutoDIR: Automatic All-in-One Image Restoration with Latent Diffusion](https://mlsanity.com/paper/2310.10123/) (2023) - [MambaIRv2: Attentive State Space Restoration](https://mlsanity.com/paper/2411.15269/) (2024) - [DEA-Net: Single image dehazing based on detail-enhanced convolution and content-guided attention](https://mlsanity.com/paper/2301.04805/) (2023) - [Perceive-IR: Learning to Perceive Degradation Better for All-in-One Image Restoration](https://mlsanity.com/paper/2408.15994/) (2024) - [Neural Degradation Representation Learning for All-In-One Image Restoration](https://mlsanity.com/paper/2310.12848/) (2023) - [Toward Real-world Single Image Deraining: A New Benchmark and Beyond](https://mlsanity.com/paper/2206.05514/) (2022) - [MSP-Former: Multi-Scale Projection Transformer for Single Image Desnowing](https://mlsanity.com/paper/2207.05621/) (2022) - [Vision-Language Gradient Descent-driven All-in-One Deep Unfolding Networks](https://mlsanity.com/paper/2503.16930/) (2025) ## Built on by (most cited first, 2 of 2) - [Learning to Restore More: Continual Capability Expansion for Pretrained Image Restoration Models](https://mlsanity.com/paper/2608.30305/) (2026) - [TIRMamba: A Thermal-Prior-Modulated State-Space Network for Sub-Million-Parameter Infrared Image Super-Resolution](https://mlsanity.com/paper/2610.05182/) (2026) ## Abstract (arXiv) Image restoration aims to recover high-quality images from degraded observations. Recent Mamba-based image restoration models have demonstrated strong potential in modeling long-range dependencies with linear complexity. However, most existing designs still rely on a single state-evolution timescale, which limits their adaptability to spatially heterogeneous and task-dependent degradation patterns in all-in-one image restoration. In this paper, we propose Multi-τ Liquid-Mamba, an adaptive state space module that introduces input-conditioned multi-timescale liquid discretization into selective state space modeling. Instead of changing the overall selective scan pipeline, the proposed module modulates the effective discretization steps of multiple dynamical branches and adaptively fuses their responses according to degradation-aware gating weights. This design allows the model to capture both fast-varying local details and slowly evolving global structures while preserving the linear scaling property of Mamba with respect to sequence length. Importantly, Multi-τ Liquid-Mamba modulates the effective transition dynamics while preserving the original selective parameterization and hardware-efficient selective scan mechanism, making it a plug-and-play module that can be seamlessly integrated into existing Mamba-based architectures. Built upon this framework, we develop a Multi-τ Liquid-Mamba Image Restoration Network (MLMIR) for all-in-one image restoration. Extensive experiments on a wide range of restoration benchmarks demonstrate that MLMIR consistently achieves state-of-the-art performance in all-in-one image restoration while remaining highly competitive in task-aligned restoration settings.