High-throughput chromosome conformation capture (Hi-C) experiments are typically performed on a large population of cells and therefore only yield average numbers of genomic contacts. Nevertheless population Hi-C data are often interpreted in terms of a single genomic structure, which ignores all cell-to-cell variability. We propose a probabilistic, statistically rigorous method to infer chromatin structure ensembles from population Hi-C data that takes the ensemble nature of the data explicitly into account and allows us to infer the number of structures required to explain the data.In recent years, chromosome conformation capture (3C) methods have emerged as a powerful tool to investigate the three-dimensional organization of genomes on previously inaccessible length scales.Thanks to experimental advances and decreasing sequencing costs, genome-wide 3C methods such as Hi-C (1) and Hi-C variants (2; 3) have yielded contact maps with resolutions of up to 1 kb. Highresolution contact maps have provided fascinating insights into the organization of chromatin domains and compartments of various sizes and their role in gene regulation (1; 4; 5; 6; 3).Although Hi-C can be performed in single cells (7; 8; 9; 10; 11), much richer data are usually obtained by analyzing populations of cells at the price of a more difficult interpretation of the data:Contact maps obtained in population Hi-C experiments show an average over millions of cells. Given that single-cell Hi-C experiments revealed significant structural variability among cell nuclei (7), it remains difficult to assess the information content and degree of structural heterogeneity reflected by population Hi-C data.1 Much effort has gone into the development of chromatin structure determination approaches, in which a single consensus structure is calculated (12). In light of recent results on cell-to-cell variability and considering experimental limitations and biases, consensus structure approaches are fundamentally limited, if not flawed (13). Several approaches taking into account the heterogeneity of cell populations have been explored. Matrix deconvolution has been used to unmix Hi-C matrices without explicitly modeling 3D structures (14; 15). While some structural information is already apparent in contact matrices, it is useful to find an approximate 3D representation giving rise to the data. For example, a 3D chromosome model allows the detection of three-way interactions not accessible in 3C data (16). Furthermore, data from other sources (e.g., imaging) can be included in the modeling process. A second approach is thus to calculate an ensemble of structures that reflect the structural heterogeneity of chromosomes more realistically than consensus structure approaches and reproduce the contact map only on average. This can be achieved in two different ways: First, one can optimize a set of structures generated from a polymer model so as to reproduce, on average, the experimental data (2; 17; 18; 19). A second possibility is to adjust the parameters of a pol...