In a general Deep Neural Network (DNN)-based beat and downbeat tracking pipeline, a post-processing stage is required to refine the beat/downbeat posteriors estimated by the DNN. A widely used post-processing method is to infer the beat/downbeat sequence that maximizes the likelihood of a probabilistic model such as the Dynamic Bayesian Network (DBN). In this work, we aim to train a DNN that can directly estimate consistent beat/downbeat posteriors without the need for post-processing. We adopt regularization approach that minimizes the difference between the DNN and the DBN. We experimentally show that the DNN trained with the regularization loss can estimate beat and downbeat posteriors with higher temporal consistency, reducing the need for post-processing.