Abnormal behaviors in industrial systems may be early warnings on critical events that may cause severe damages to facilities and security. Thus, it is important to detect abnormal behaviors accurately and timely. However, the anomaly detection problem is hard to solve in practice, mainly due to the rareness and the expensive cost to get the labels of the anomalies. Deep generative models parameterized by neural networks have achieved state-of-the-art performance in practice for many unsupervised and semisupervised learning tasks. We present a new deep generative model, Latent Enhanced regression/classification Deep Generative Model (LEDGM), for the anomaly detection problem with multidimensional data. Instead of using two-stage decoupled models, we adopt an end-to-end learning paradigm. Instead of conditioning the latent on the class label, LEDGM conditions the label prediction on the learned latent so that the optimization goal is more in favor of better anomaly detection than better reconstruction that the previously proposed deep generative models have been trained for. Experimental results on several synthetic and real-world small- and large-scale datasets demonstrate that LEDGM can achieve improved anomaly detection performance on multidimensional data with very sparse labels. The results also suggest that both labeled anomalies and labeled normal are valuable for semisupervised learning. Generally, our results show that better performance can be achieved with more labeled data. The ablation experiments show that both the original input and the learned latent provide meaningful information for LEDGM to achieve high performance.