Metal additive manufacturing (AM) has been receiving unprecedented attention for its transformational role in extending the AM materials from polymers to various metals. However, various quality issues, especially porosity, significantly impacts the mechanical properties and fatigue life of the final products, which imposes barriers for the widespread adoption of metal AM processes. In this study, we use the deep learning (DL) techniques to comprehensively investigate the relationships between pore microstructure and processing parameters. Specifically, a novel hybrid deep generative prediction network (HDGPN) that leverages both variational autoencoder and generative adversarial network is proposed to characterize the complex pore microstructure with in-depth representations and predict pore morphology under arbitrary processing parameters. By visualizing the predicted pore morphology, the complicated interaction dynamics between the processing parameters and pore microstructure are directly revealed, which may guide the optimization of metal AM manufacturing processes to fabricate defect-free products. A case study of a selective laser melting (SLM) process is conducted to validate the proposed modeling and prediction framework.