  Continuous normalizing flows (CNFs) construct invertible mappings between an
arbitrary complex distribution and an isotropic Gaussian distribution using
Neural Ordinary Differential Equations (neural ODEs). It has not been tractable
on large datasets due to the incremental complexity of the neural ODE training.
Optimal Transport theory has been applied to regularize the dynamics of the ODE
to speed up training in recent works. In this paper, a temporal optimization is
proposed by optimizing the evolutionary time for forward propagation of the
neural ODE training. In this appoach, we optimize the network weights of the
CNF alternately with evolutionary time by coordinate descent. Further with
temporal regularization, stability of the evolution is ensured. This approach
can be used in conjunction with the original regularization approach. We have
experimentally demonstrated that the proposed approach can significantly
accelerate training without sacrifying performance over baseline models.
