This paper presents a deep generative model for capturing the conditional probability distribution of future wind power given its history by modeling and pattern recognition in a dynamic graph. The dynamic nodes show the wind sites while the dynamic edges reflect the correlation between the nodes. We propose a scalable optimization model, which is theoretically proved to catch distributions at nodes of the graph, contrary with all learning formulations in the sector of discriminatory pattern recognition. The density of probabilities for each node can be used as samples in our framework. This probabilistic deep convolutional Auto-encoder (PDCA), is based on the deep learning of localized first-order approximation of spectral graph convolutions, a novel evolutionary algorithm and the Bayesian variational inference concepts. The presented generative model is used for the spatiotemporal probabilistic wind power problem in a wide 25 wind sites located in California, the USA for up to 24 hr ahead prediction. The experimental findings reveal that our proposed model outperforms other competitive temporal and spatio-temporal algorithms in terms of reliability, sharpness, and continuous ranked probability score.