scHiDiffEM: Reconstructing Sparse Single-Cell Hi-C Contact Maps with Diffusion Expectation–Maximization

Single-cell Hi-C (scHi-C) profiling elucidates three-dimensional (3D) genome architecture at cellular resolution, yet individual contact maps are severely corrupted by extreme count sparsity, cell-to-cell sequencing depth heterogeneity, and power-law genomic distance decay. An observed zero conflates true biological non-contact with technical sampling dropout, making it difficult to reconstruct cell-specific topology without averaging away biological variation. We introduce scHiDiffEM (Single-Cell Hi-C Diffusion Expectation–Maximization), which treats reconstruction as a population-informed inverse problem. A distance-aware low-rank decoder represents chromosome contact rates, and a library-size-normalized negative-binomial model relates these rates directly to raw counts. With clean single-cell targets unavailable, depth-normalized mini-pseudo-bulks from unsupervised subpopulations supply canonical seeds to initialize a population-conditioned diffusion prior. A generalized expectation–maximization (EM) framework then jointly trains the model: the E-step restores individual single-cell latents via raw-count data consistency and bounded diffusion proximal updates, while sequential M-steps iteratively optimize the observation likelihood parameters and refine the diffusion prior. Across 18 independent benchmark datasets spanning five biological collections, scHiDiffEM substantially improves overall performance across cell embeddings, contact-pattern imputation, and topological structure recovery without dataset-specific tuning. These results establish scHiDiffEM as a principled framework for scHi-C reconstruction, enabling faithful recovery of single-cell chromatin architecture from extreme sparsity without requiring unattainable ground truth.