Generative models achieve tremendous success for natural image processing and generation. It also provides new solution for many classic medical image processing tasks. In this talk, I will introduce two medical imaging tasks: image reconstruction and image synthesis based on normalized flow (NF). First, we incorporate NF prior and proposed a class of Langevin-based sampling algorithms, namely NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm) for Bayesian inverse problems. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various imaging problems, including limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is shown to be effective, especially for severely ill-posed inverse problems. Secondly, medical image synthesis aims to generate an unacquired image modality, often from other observed data modalities. We propose an optimal transport and NF-based approach to find a transformation between two unknown probability distributions from samples. By minimizing the symmetric maximum mean discrepancy (MMD) between samples from two unknown distributions and an optimal transport cost as regularization to obtain a short-distance and interpretable transformation. The resulted transformation leads to more stable and accurate sample generation. We establish some theoretical results for the proposed model and demonstrate its effectiveness with low-dimensional illustrative examples as well as high-dimensional medical image generative samples.