Chromosome conformation capture technologies such as Hi-C are widely used to investigate the spatial organization of genomes. Because genome structures can vary considerably between individual cells of a population, interpreting ensemble-averaged Hi-C data can be challenging, in particular for long-range and interchromosomal interactions. We pioneered a probabilistic approach for the generation of 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, which runs on local machines (for practice runs) and high-performance computing platforms. PGS takes a genome-wide Hi-C contact frequency matrix, along with information about genome segmentation, and produces an ensemble of 3D genome structures entirely consistent with the input. The software automatically generates an analysis report, and provides tools to extract and analyze the 3D coordinates of specific domains. Basic Linux command-line knowledge is sufficient for using this software. A typical running time of the pipeline is ∼3 d with 300 cores on a computer cluster to generate a population of 1,000 diploid genome structures at topological-associated domain (TAD)-level resolution.