Learning Adaptive Dynamical Features via Multi-τ Liquid-Mamba for All-in-one Image Restoration

Existing Mamba-based image restoration models typically rely on a single, fixed timescale for state evolution. This limitation prevents them from effectively adapting to the diverse, spatially heterogeneous degradation patterns (e.g., noise, blur, rain, haze) encountered in all-in-one image restoration tasks. The authors investigate whether introducing multi-timescale, input-dependent dynamics can enhance the model's ability to handle these varied degradations without sacrificing the linear complexity of the Mamba architecture.

The authors propose the Multi-τ Liquid-Mamba, a plug-and-play module that integrates continuous-time liquid neural dynamics into the selective state space modeling framework. Instead of using a single discretization branch, the module employs multiple dynamical branches with learnable time constants. These branches are modulated by input-conditioned gating weights, allowing the model to dynamically fuse responses based on local image content. This design enables the system to capture both fast-varying local details and slowly evolving global structures. The authors then integrate this module into a hierarchical encoder-decoder architecture, termed the Multi-τ Liquid-Mamba Image Restoration Network (MLMIR).

• The Multi-τ Liquid-Mamba module successfully enables content-aware state transitions, allowing the hidden-state dynamics to evolve at different rates across different image regions.
• The MLMIR architecture achieves state-of-the-art performance across a wide range of all-in-one and task-aligned image restoration benchmarks.
• The proposed framework maintains the hardware-efficient selective scan mechanism and linear scaling properties of standard Mamba models, making it a seamless, plug-and-play upgrade for existing architectures.