continuous updates of the PES. The suggested TD-ADGA is a generalization of the previous ADGA (TI-ADGA) where the evolving nuclear density is put central in the decisions of when and where to update the PES with new SPs. We have verified the approach for both single-and double-minimum PESs, one-and multi-dimensional PESs, and with and without time-dependent terms in the Hamiltonian. In all cases, the results obtained with TD-ADGA are near to the results obtained in reference computations where extensive reference PESs have been used. In particular, an approach where first the whole dynamics is studied with a partial restart followed by a final full restart dynamics calculation has shown a high level of agreement with the results of accurate reference computations. We believe the method opens a whole new framework for computing quantum dynamics accurately, also for larger systems.