A method for diabatising multiple electronic states on-the-fly within the direct dynamics variational multi-configuration Gaussian method for calculating quantum nuclear dynamics is presented. The method is based upon the propagation of the adiabatic-diabatic transformation matrix along the paths followed by the Gaussian basis functions that constitute the nuclear wave function, by use of a well-known differential equation relating the matrix and the nonadiabatic vector coupling terms between the electronic states. The implementation of the method is described, and test calculations are presented using the ground and first-excited states of the butatriene cation as an example, allowing comparison to the earlier regularisation diabatisation scheme as well as to full nuclear dynamics on a precomputed potential energy surface. The new scheme is termed propagation diabatisation.