Hi-C technologies are widely used to investigate the spatial organization of genomes. However, the structural variability of the genome is a great challenge to interpreting ensemble-averaged Hi-C data, particularly for long-range/interchromosomal interactions. We pioneered a probabilistic approach for generating a population of distinct diploid 3D genome structures consistent with all the chromatin-chromatin interaction probabilities from Hi-C experiments. Each structure in the population is a physical model of the genome in 3D. Analysis of these models yields new insights into the causes and the functional properties of the genome's organization in space and time. We provide a user-friendly software package, called PGS, that runs on local machines and high-performance computing platforms. PGS takes a genome-wide Hi-C contact frequency matrix and produces an ensemble of 3D genome structures entirely consistent with the input. The software automatically generates an analysis report, and also provides tools to extract and analyze the 3D coordinates of specific domains.