Ductal carcinoma in situ (DCIS) is a risk factor for subsequent invasive breast cancer (IBC). To identify events in DCIS that lead to invasive cancer, we performed single-cell RNA sequencing on DCIS lesions and matched normal breast tissue. Inferred copy-number variation was used to identify neoplastic epithelial cells from clinical specimens, which contained a mixture of DCIS and normal ducts. Phylogenetic analysis demonstrated intratumoral clonal heterogeneity that was associated with significant gene expression differences. Classification of epithelial cells into mammary cell states revealed that subclones contained a mixture of cell states, suggesting an ongoing pattern of differentiation after neoplastic transformation. Cell state proportions were significantly different based on estrogen receptor expression, with estrogen receptor-negative DCIS more closely resembling the distribution in the normal breast, particularly with respect to cells with basal characteristics. Specific alterations in cell state proportions were associated with progression to invasive cancer in a cohort of DCIS with longitudinal outcome. Ongoing transcription of key basement membrane (BM) genes occurred in specific subsets of epithelial cell states, including basal/myoepithelial, which are diminished in DCIS. In the transition to IBC, the BM protein laminin, but not COL4, was altered in DCIS adjacent to invasion. Loss of COL4, but not laminin, in an in vitro DCIS model led to an invasive phenotype. These findings suggest that the process of invasion is a loss-of-function event due to an imbalance in critical cell populations essential for BM integrity rather than a gain of an invasive phenotype by neoplastic cells. SIGNIFICANCE: Single-cell analyses reveal ductal carcinoma in situ comprises multiple genetic clones with significant phenotypic diversity and link alterations in epithelial cell states and basement membrane integrity with invasive breast cancer progression.