Abstract The problem of 3D chromosome structure inference from Hi-C datasets is important and challenging. While bulk Hi-C datasets contain contact information derived from millions of cells, and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named SIMBA3D, to infer 3D structures of chromosomes from single cell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C dataset as a function of prior strength and demonstrate clustering of solutions using data from the same cell.