Lack of standardization and various intrinsic parameters for magnetic resonance (MR) image acquisition results in heterogeneous images across different sites and devices, which adversely affects the generalization of deep neural networks. To alleviate this issue, this work proposes a novel unsupervised harmonization framework that leverages normalizing flows to align MR images, thereby emulating the distribution of a source domain. The proposed strategy comprises three key steps. Initially, a normalizing flow network is trained to capture the distribution characteristics of the source domain. Then, we train a shallow harmonizer network to reconstruct images from the source domain via their augmented counterparts. Finally, during inference, the harmonizer network is updated to ensure that the output images conform to the learned source domain distribution, as modeled by the normalizing flow network. Our approach, which is unsupervised, source-free, and task-agnostic is assessed in the context of both adults and neonatal cross-domain brain MRI segmentation, as well as neonatal brain age estimation, demonstrating its generalizability across tasks and population demographics. The results underscore its superior performance compared to existing methodologies. The code is available at https://github.com/farzad-bz/Harmonizing-Flows
