Event cameras or dynamic vision sensors (DVS) record asynchronous response to brightness changes instead of conventional intensity frames, and feature ultra-high sensitivity at low bandwidth. The new mechanism demonstrates great advantages in challenging scenarios with fast motion and large dynamic range. However, the recorded events might be highly sparse due to either limited hardware bandwidth or extreme photon starvation in harsh environments. To unlock the full potential of event cameras, we propose an inventive event sequence completion approach conforming to the unique characteristics of event data in both the processing stage and the output form. Specifically, we treat event streams as 3D event clouds in the spatiotemporal domain, develop a diffusion-based generative model to generate dense clouds in a coarse-to-fine manner, and recover exact timestamps to maintain the temporal resolution of raw data successfully. To validate the effectiveness of our method comprehensively, we perform extensive experiments on three widely used public datasets with different spatial resolutions, and additionally collect a novel event dataset covering diverse scenarios with highly dynamic motions and under harsh illumination. Besides generating high-quality dense events, our method can benefit downstream applications such as object classification and intensity frame reconstruction.