The fields of physical chemistry and chemical physics have sparkled with ideas for novel developments to study processes in the strong light-matter coupling regime, reformulating in cavities concepts such as the BO approximation and nonadiabatic dynamics . In this respect, the exact factorization appears to be an extremely well adapted formalism to gain new insights into the correlated PEN dynamics and to develop simulation algorithms, in the spirit of similar efforts using surface hopping and the Ehrenfest scheme.