Existing full-reference image quality assessment (FR-IQA) methods achieve high-precision evaluation by analysing feature differences between reference and distorted images. However, their performance is constrained by the quality of the reference image, which limits real-world applications where ideal reference sources are unavailable. Notably, the human visual system has the ability to accumulate visual memory, allowing image quality assessment on the basis of long-term memory storage. Inspired by this biological memory mechanism, we propose a memory-driven quality-aware framework (MQAF), which establishes a memory bank for storing distortion patterns and dynamically switches between dual-mode quality assessment strategies to reduce reliance on high-quality reference images. When reference images are available, MQAF obtains reference-guided quality scores by adaptively weighting reference information and comparing the distorted image with stored distortion patterns in the memory bank. When the reference image is absent, the framework relies on distortion patterns in the memory bank to infer image quality, enabling no-reference quality assessment (NR-IQA). The experimental results show that our method outperforms state-of-the-art approaches across multiple datasets while adapting to both no-reference and full-reference tasks.