Abstract: Unpaired image-to-image translation aims to translate an input image to another domain such that the output image looks like an image from another domain while important semantic information are preserved. Inferring the optimal mapping with unpaired data is impossible without making any assumptions. In this paper, we make a density changing assumption where image patches of high probability density should be mapped to patches of high probability density in another domain. Then we propose an efficient way to enforce this assumption: we train the flows as density estimators and penalize the variance of density changes. Despite its simplicity, our method achieves the best performance on benchmark datasets and needs only $56-86\%$ of training time of the existing state-of-the-art method. The training and evaluation code are avaliable at $$\url{https://github.com/Mid-Push/Decent}.$$