This paper addresses the problem of Speaker Recognition (SR) systems' vulnerability to acoustic variations and speech distortions. We introduce FM-SEE: Flow Matching-based Speaker Embedding (SE) Enhancer, a flow-based approach that improves SR robustness without computational overhead. Given a teacher SR system, our method refines SEs, making them more reliable and robust. Furthermore, we show that FM-SEE's generative nature can be used to model target score distributions in order to compute LLR scores. Thus we introduce a new score normalization method that is integrated with FM-SEE. Despite being trained on a relatively small tuning set (only the VoxCeleb1,2 devsets), FM-SEE demonstrates substantial performance gains on challenging acoustic scenarios (SRE'21,'24) compared to the teacher model. We evaluate the proposed SR system on seven datasets, and it achieves average relative improvements of 17% and 11% over the teacher model in terms of EER and minDCF(0.01), respectively.