With the increased density and the technology scaling, flash memory is more vulnerable to noise effects, overwhelmingly lowering the data retention time. The periodic data refresh technique is commonly used to retain the long-term data integrity. However, the frequent refresh requests introduce the increased access conflict and severe write amplification, leading to suboptimal performance and lifetime improvement of flash memory-based storage systems. In this article, we propose ApproxRefresh, which enables the uncorrectable data reuse with the assistance of approximate-computing applications to reduce the refresh costs. Specifically, we design a lightweight remapping-free refresh technique, called RFR, to periodically correct, compute an enhanced ECC, and only remap new ECC parity bits, which dramatically reduces the refresh costs. Then, with approximate-read and precise-read hotness awareness, ApproxRefresh selectively adopts RFR or the traditional remapping-based refresh technique to reduce the refresh costs and the read disturbance. Besides, ApproxRefresh further improves flash access performance based on data hotness and process variations. In addition, a corresponding ApproxRefresh-aware garbage collection algorithm is proposed to complete the design. Evaluations show that ApproxRefresh reduces the refresh latency by 36.19% over the state of the art.