This paper introduces a novel framework for image quality transfer based on conditional flow matching (CFM). Unlike conventional generative models that rely on iterative sampling or adversarial objectives, CFM learns a continuous flow between a noise distribution and target data distributions through the direct regression of an optimal velocity field. We evaluate this approach in the context of low-field magnetic resonance imaging (LF-MRI), a rapidly emerging modality that offers affordable and portable scanning but suffers from inherently low signal-to-noise ratio and reduced diagnostic quality. Our framework is designed to reconstruct high-field-like MR images from their corresponding low-field inputs, thereby bridging the quality gap without requiring expensive infrastructure. Experiments demonstrate that CFM not only achieves state-of-the-art performance, but also generalizes robustly to both in-distribution and out-of-distribution data. Importantly, it does so while utilizing significantly fewer parameters than competing deep learning methods. These results underline the potential of CFM as a powerful and scalable tool for MRI reconstruction, particularly in resource-limited clinical environments.