Conformation capture technologies (e.g., Hi-C) chart physical interactions between chromatin regions on a genome-wide scale. However, the structural variability of the genome between cells poses a great challenge to interpreting ensemble-averaged Hi-C data, particularly for long-range and interchromosomal interactions. Here, we present a probabilistic approach for deconvoluting Hi-C data into a model population of distinct diploid 3D genome structures, which facilitates the detection of chromatin interactions likely to co-occur in individual cells. Our approach incorporates the stochastic nature of chromosome conformations and allows a detailed analysis of alternative chromatin structure states. For example, we predict and experimentally confirm the presence of large centromere clusters with distinct chromosome compositions varying between individual cells. The stability of these clusters varies greatly with their chromosome identities. We show that these chromosome-specific clusters can play a key role in the overall chromosome positioning in the nucleus and stabilizing specific chromatin interactions. By explicitly considering genome structural variability, our population-based method provides an important tool for revealing novel insights into the key factors shaping the spatial genome organization. (14), and single-cell (15) and in situ Hi-C (16)], close chromatin contacts can now be identified at increasing resolution, providing new insight into genome organization. These methods measure the relative frequencies of chromosome interactions averaged over a large population of cells. However, individual 3D genome structures can vary dramatically from cell to cell even within an isogenic sample, especially with respect to long-range interactions (15,17,18). This structural variability poses a great challenge to the interpretation of ensemble-averaged Hi-C data (14,(19)(20)(21)(22)(23) and prevents the direct detection of cooperative interactions co-occurring in the same cell. This problem is particularly evident for long-range (cis) and interchromosomal (trans) interactions, which are generally observed at relatively low frequencies and are therefore present only in a small subset of individual cells at any given time (3,11,15). Despite their low frequencies, long-range and interchromosome interaction patterns are not random noise. In fact, these interactions are more informative than short-range interactions in determining the global genome architectures in cells and are often functionally relevant-interactions between transcriptionally active regions are often interchromosomal in nature (14). Owing to their variable nature, long-range and trans interactions can be part of alternative, structurally different conformations, which makes their interpretation in form of consensus structures impossible. However, inferring which of the long-range interactions co-occur in the same cell from ensemble Hi-C data remains a major challenge.These challenges cannot be easily overcome even by the new single-cell Hi-C techno...