The digitalization of cores, namely the reconstruction of digital cores, is a method to reflect the real internal structures of cores by reconstructing the microstructural information and describing the microstructure of cores on the pore scale, which has become an effective way of quantitatively analyzing the pore structures and other matters in cores for rock physics and petroleum science. The modeling method of digital cores can be divided into the physical experimental methods and numerical simulation methods. Physical experimental methods usually are time-consuming and expensive because the drilling and core sampling for physical experiments are quite costly and the manufacturing of experimental samples sometimes are difficult to implement. Without the complex physical preparation and the demands for expensive equipment, numerical simulation methods are relatively cost-effective but still suffer from a lengthy processing time. Recently, deep learning and its variants can effectively extract characteristics from training images (TIs), casting light on the fast reconstruction of digital cores. In this paper, a reconstruction method is proposed by combining the variational auto-encoder (VAE) and the generative adversarial network (GAN) to achieve the balance of their strengths and weaknesses. Besides, the learning diverse generations using determinantal point processes (GDPP) is added to improve the quality of the generated results. Compared to some numerical simulation methods and GAN, the effectiveness and practicability of the proposed method are demonstrated. • The reconstruction quality by our method is better than GAN. • Our method can save and reuse model parameters for other reconstructions. • Our method is suitable for large-quantity reconstructions.