During the last ten years, many research results have been referring to a particular type of cancer-associated fibroblasts associated with poor prognosis, invasiveness, metastasis and resistance to therapy in multiple cancer types, characterized by a gene expression signature with prominent presence of genes COL11A1, THBS2 and INHBA. Identifying the underlying biological mechanisms responsible for their creation may facilitate the discovery of targets for potential pan-cancer therapeutics. Using a novel computational approach for single-cell gene expression data analysis identifying the dominant cell populations in a sequence of samples from patients at various stages, we conclude that these fibroblasts are produced by a pan-cancer cellular transition originating from a particular type of adipose-derived stromal cells naturally present in the stromal vascular fraction of normal adipose tissue, having a characteristic gene expression signature. Focusing on a rich pancreatic cancer dataset, we provide a detailed description of the continuous modification of the gene expression profiles of cells as they transition from APOD-expressing adipose-derived stromal cells to COL11A1-expressing cancer-associated fibroblasts, identifying the key genes that participate in this transition. These results also provide an explanation to the well-known fact that the adipose microenvironment contributes to cancer progression.