Epigenetic reprogramming is a critical event in the generation of induced pluripotent stem cells (iPSCs). Although the iPSCs from different sources are very similar to each other and to embryonic stem cells (ESCs), there are epigenetic differences in small fraction. iPSCs become epigenetically closer to each other with continuous passaging even though they have been derived from different cell types; human amnion, endometrium and menstrual blood cells. However, iPSCs exhibit distinct epigenetic distances from ESCs at early passages. Continuous passaging of the iPSCs diminishes the differences between iPSCs and ESCs via periodic aberrant hyper-methylation. This aberrant stochastic hyper-methylation and their convergence is a direct cause of the transgene-independent phases of iPS reprogramming. The number of passages for “convergence” of the aberrant hyper-methylation is dependent on the parental cell type. Interestingly, the amnion-derived-iPSCs show a more rapid decrease in the number of aberrant methylated sites during additional cultivation than endometrium-derived-iPSCs and menstrual blood cell-derived-iPSCs. Amnion cells offer additional benefits; they can be collected in a non-invasive manner and can be frozen and stored by conventional methods. Therefore, they are a strong candidate cell source for iPSC generation for clinical applications.