The mammalian genome is highly organized within the cell nucleus. The nuclear position of many genes and genomic regions changes during physiological processes such as proliferation, differentiation, and disease. It is unclear whether disease-associated positioning changes occur specifically or are part of more global genome reorganization events. Here, we have analyzed the spatial position of a defined set of cancer-associated genes in an established mammary epithelial three-dimensional cell culture model of the early stages of breast cancer. We find that the genome is globally reorganized during normal and tumorigenic epithelial differentiation. Systematic mapping of changes in spatial positioning of cancer-associated genes reveals gene-specific positioning behavior and we identify several genes that are specifically repositioned during tumorigenesis. Alterations of spatial positioning patterns during differentiation and tumorigenesis were unrelated to gene activity. Our results demonstrate the existence of activity-independent genome repositioning events in the early stages of tumor formation.