Trajectory inference has important applications. In particular, biological development can be interpreted as a curve in the space of distributions of gene expressions, where one wants to infer such a curve from the sample data. There has been progress in this direction by using optimal transport (OT) as a way to interpolate different distributions, e.g. the work of Schiebinger et al. In this talk we discuss stability of such OT based method. This is joint work in progress with Geoff Schiebinger and Rentian Yao.