The synchronization problem of the coupled delayed inertial neural networks (DINNs) with stochastic delayed impulses is studied. Based on the properties of stochastic impulses and the definition of average impulsive interval (AII), some synchronization criteria of the considered DINNs are obtained in this article. In addition, compared with previous related works, the requirement on the relationship among the impulsive time intervals, system delays, and impulsive delays is removed. Furthermore, the potential effect of impulsive delay is studied by rigorous mathematical proof. It is shown that within a certain range, the larger the impulsive delay, the faster the system converges. Numerical examples are provided to show the correctness of the theoretical results.