Traffic flow prediction plays a critical role in reducing traffic congestion in transportation systems. However, accurate traffic flow prediction becomes challenging due to the impact of complex spatio-temporal (ST) correlations and the diversity of ST correlations. When modeling complicated ST correlations, researchers usu did not take the diversity of ST correlations into consideration, resulting in poor prediction accuracy. In this paper, we propose ST-InNet, a deep spatio-temporal Inception network for collectively predicting traffic flow in each city region. Specifically, ST-InNet employs two Inception networks to simultaneously capture various spatial and temporal correlations of traffic data, including temporal closeness, temporal periodicity, nearby spatial dependencies, and distant spatial dependencies. For the diversity of spatial correlations, ST-InNet presents an improved variant of an Inception module to explicitly capture the different contributions of spatial correlations for each region. For the diversity of temporal correlations, ST-InNet designs a fusion component to explicitly model the varying contributions of temporal correlations on prediction. The experiments are conducted on a real-world traffic dataset in Nanjing, demonstrating that ST-InNet outperforms five state-of-the-art baselines in short-term and long-term traffic flow predictions with an average accuracy improvement of 32.09% and 30.97%, respectively.