Voice conversion (VC) using artificial neural networks (ANNs) has shown its capability to produce better sound quality of the converted speech than that using Gaussian mixture model (GMM). Although ANN-based VC works reasonably well, there is still room for further improvement. One of the promising ways is to adopt the successful techniques in statistical model-based parameter generation (SMPG), such as trajectory-based mapping approaches that are originally designed for GMM-based VC and hidden Markov model (HMM)-based speech synthesis. This study presents a probabilistic interpretation for ANN-based VC. In this way, ANN-based VC can easily incorporate the successful techniques in SMPG. Experimental results demonstrate that the performance of ANN-based VC can be effectively improved by two trajectory-based mapping techniques (maximum likelihood parameter generation (MLPG) algorithm and maximum likelihood-based trajectory mapping considering global variance (referred to as MLGV)), compared to the conventional ANN-based VC with frame-based mapping and the GMM-based VC with the MLPG algorithm. Moreover, ANN-based VC with the trajectory-based mapping techniques can achieve comparable performance when compared to the state-of-the-art GMM-based VC with the MLGV algorithm.