Soft sensors have been extensively developed and applied in the process industry. One of the main challenges of the data-driven soft sensors is the lack of labeled data and the need to absorb the knowledge from a related source operating condition to enhance the soft sensing performance on the target application. This article introduces deep transfer learning to soft sensor modeling and proposes a deep probabilistic transfer regression (DPTR) framework. In DPTR, a deep generative regression model is first developed to learn Gaussian latent feature representations and model the regression relationship under the stochastic gradient variational Bayes framework. Then, a probabilistic latent space transfer strategy is designed to reduce the discrepancy between the source and target latent features such that the knowledge from the source data can be explored and transferred to enhance the target soft sensor performance. Besides, considering the missing values in the process data in the target operating condition, the DPTR is further extended to handle the missing data problem utilizing the strong generation and reconstruction capability of the deep generative model. The effectiveness of the proposed method is validated through an industrial multiphase flow process.