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In this paper, we propose an approach to effectively accelerating thecomputation of continuous normalizing flow (CNF), which has been proven to be apowerful tool for the tasks such as variational inference and densityestimation. The training time cost of CNF can be extremely high because therequired number of function evaluations (NFE) for solving correspondingordinary differential equations (ODE) is very large. We think that the high NFEresults from large truncation errors of solving ODEs. To address the problem,we propose to add a regularization. The regularization penalizes the differencebetween the trajectory of the ODE and its fitted polynomial regression. Thetrajectory of ODE will approximate a polynomial function, and thus thetruncation error will be smaller. Furthermore, we provide two proofs and claimthat the additional regularization does not harm training quality. Experimentalresults show that our proposed method can result in 42.3% to 71.3% reduction ofNFE on the task of density estimation, and 19.3% to 32.1% reduction of NFE onvariational auto-encoder, while the testing losses are not affected.

Accelerating Continuous Normalizing Flow with Trajectory Polynomial Regularization