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