Underwater image enhancement, especially in color restoration and detail reconstruction, remains a significant challenge. Current models focus on improving accuracy and learning efficiency through neural network design, often neglecting traditional optimization algorithms’ benefits. We propose FAIN-UIE, a novel approach for color and fine-texture recovery in underwater imagery. It leverages insights from the Fast Iterative Shrink-Threshold Algorithm (FISTA) to approximate image degradation, enhancing network fitting speed. FAIN-UIE integrates the residual degradation module (RDM) and momentum calculation module (MC) for gradient descent and momentum simulation, addressing feature fusion losses with the Feature Merge Block (FMB). By integrating multi-scale information and inter-stage pathways, our method effectively maps multi-stage image features, advancing color and fine-texture restoration. Experimental results validate its robust performance, positioning FAIN-UIE as a competitive solution for practical underwater imaging applications.