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We study the influence of diversity on the dynamics of spiking in spatially extended systems with global or diffusive couplings, which is locally modeled by a map-based neuron. The variance of the system’s parameter D is used to measure the diversity. It is found that the regularity of spikes reaches a maximum with a variation in D, indicating the occurrence of diversity-induced coherence resonance. Moreover, diversity-induced coherence resonance in this system can be greatly enhanced by increasing the coupling strength. Our analysis shows that these phenomena have inherent relevance to both the bifurcation feature of a single neuron and interaction through couplings. These results may exhibit that diversity plays a constructive role in enhancing the time precision of firing in a neural network.