Chromatin conformation capture technologies have revealed the complex 3D organizationof the genome and its key regulatory role. Single-cell Hi-C (scHi-C) maps this architectureat single-cell level, but its sparse nature makes data interpretation challenging, and tools fortheir analysis remain limited. Here, we present a physics-based framework that combinespolymer modeling with computational methods to reconstruct full 3D genome structuresfrom sparse scHi-C data. Using both artificial and experimental data, we show that ourapproach imputes missing contacts and recovers accurate structures validated againstindependent Hi-C and established polymer models. Applied to scHi-C from a 15 Mbregion of human HeLa-S3 cells as a case study, the method uncovers distinct structuralclasses defined by the spatial distribution of chromatin binding domains. The reconstructedmodels enable robust downstream analyses, including the identification of single-celltopologically associated domains (TADs), which appear highly variable across cells yet tendto accumulate around those observed in bulk. Importantly, the inferred 3D polymer modelscapture diverse epigenetic signatures, with active chromatin domains exhibiting greaterstructural variability than repressive ones across single cells. Overall, our study providesa mechanistic and interpretable framework to analyze sparse scHi-C data, highlightinghow polymer physics can be leveraged to uncover genome architecture and its functionalvariability at single-cell resolution.