Image clustering is one of the crucial techniques in multimedia analytics and knowledge discovery. Recently, the Deep clustering method (DC), characterized by its ability to perform feature learning and cluster assignment jointly, surpasses the performance of traditional ones on image data. However, existing methods rarely consider the role of model learning strategies in improving the robustness and performance of clustering complex image data. Furthermore, most approaches rely solely on point-to-point distances to cluster centers for partitioning the latent representations, resulting in error accumulation throughout the iterative process. In this paper, we propose a robust image clustering method (IDCL) which, to our knowledge for the first time, introduces a model training strategy using density information into image clustering. Specifically, we design a curriculum learning scheme grounded in the density information of input data, with a more reasonable learning pace. Moreover, we employ the density core rather than the individual cluster center to guide the cluster assignment. Finally, extensive comparisons with state-of-the-art clustering approaches on benchmark datasets demonstrate the superiority of the proposed method, including robustness, rapid convergence, and flexibility in terms of data scale, number of clusters, and image context.