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 at all.

翻译：在本文中,我们建议一种有效加速计算连续正常流动的方法(CNF),这已被证明是变量推断和密度估计等任务的一个有力工具。CNF的培训时间成本可能非常高,因为解决相应的普通差异方程式(ODE)所需的功能评价数量非常大。我们认为,高NFE是由于在解决 ODE 时出现大量脱轨错误造成的。为了解决这个问题,我们提议增加一个正规化。规范化惩罚ODE的轨迹与其安装的多面回归值之间的差别。ODE的轨迹将接近一个多面函数,因此脱轨错误将较小。此外,我们提供了两个证据,并声称额外的正规化不会损害培训质量。实验结果表明,我们提议的方法可以导致密度估计任务的NFE减少42.3%至71.3%,在变式自动电离子上减少NFE的19.3%至32.1%,而测试损失则不受影响。