We investigate the geodesics under the WFR metric, and propose a framework to learn the potential. In particular, a reversed KL divergence is introduced for the loss overcoming the difficulty brought by the weight. This method can be viewed as generalization of the continuous normalizing flows, and be used as a generative model for weighted samples. Such a framework might be beneficial in some applications as both the transportation and varying weights are used for the new distribution. This is an on-going work and suggestion is welcome.