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

TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speed