Propagation of clonal regulatory programs contributes to cancer development. It is poorly understood how epigenetic mechanisms interact with genetic drivers to shape this process. Here, we combine single-cell analysis of transcription and DNA methylation with a Luria-Delbrück experimental design to demonstrate the existence of clonally stable epigenetic memory in multiple types of cancer cells. Longitudinal transcriptional and genetic analysis of clonal colon cancer cell populations reveals a slowly drifting spectrum of epithelial-to-mesenchymal transcriptional identities that is seemingly independent of genetic variation. DNA methylation landscapes correlate with these identities but also reflect an independent clock-like methylation loss process. Methylation variation can be explained as an effect of global trans-acting factors in most cases. However, for a specific class of promoters-in particular, cancer-testis antigens-de-repression is correlated with and probably driven by loss of methylation in cis. This study indicates how genetic sub-clonal structure in cancer cells can be diversified by epigenetic memory.