Traditional supervised learning requires the ground truth labels for the training data, which can be difficult to collect in many cases. In contrast, crowdsourcing learning collects noisy annotations from multiple non-expert workers and infers the latent true labels through some aggregation approach. This study notices that existing deep crowdsourcing work do not sufficiently model worker correlations, which however is shown to be helpful for learning by previous non-deep learning approaches. A deep generative crowdsourcing learning model is proposed to combine the strength of deep neural networks (DNN) and at the same time exploit the worker correlations. The model comprises a DNN classifier as a priori for the true labels, and one annotation generation process in which a mixture model of workers’ reliabilities within each class is introduced for inter-worker correlation. To automatically trade-off between the model complexity and data fitting, fully Bayesian inference is developed. Based on the natural-gradient stochastic variational inference techniques developed for structured variational autoencoder (SVAE), variational message passing is combined for conjugate parameters and stochastic gradient descent for DNN under a unified framework to conduct efficient end-to-end optimization. Experimental results on 22 real world crowdsourcing data sets demonstrate the effectiveness of the proposed approach.