To achieve a more comprehensive understanding of cancer, novel computational methods are required for the integrative analysis of data from different molecular layers, such as genomics, transcriptomics, and epigenomics. Here, we present a novel multi-omics integrative method that performs unsupervised representation learning, referred to as OMIDIENT: multiOMics Integration for cancer by DIrichlet auto-ENcoder neTworks. OMIDIENT provides a natural framework for modeling sparse and compositional latent representations by employing a deep generative model, where the latent space is distributed as the product of Dirichlet distributions. Applied to five different cancers, we demonstrate that OMIDIENT outperforms the top state-of-the-art unsupervised multi-omics integrative analysis approaches in clustering, classification, and reconstruction of missing data using mRNA expression data, DNA methylation data, and microRNA expression data. Furthermore, we provide interpretability analyses for OMIDIENT that not only support its improved performance, but also offer valuable insights into the underlying structure captured by the learned representations.