We now generalize the ADGA procedure for use in quasi-direct quantum dynamics simulations, where the goal is to construct the PES during the integration of the time-dependent Schrödinger equation. As this formulation of ADGA is based on the time-dependent wave function and the corresponding evolving densities, we will term it the time-dependent adaptive density-guided approach (TD-ADGA). The construction of the TD-ADGA grid is similar to the TI-ADGA grid, where independent grids for each MC are iteratively refined by automatic placement of new SPs. However, we introduce some extra convergence criteria, since there is a fundamental difference between the TI-ADGA and TD-ADGA algorithms. In TI-ADGA, the iterations were purely algorithmic iterations until convergence (requiring of order 1-15 iterations). In the TD-ADGA, the iterations continues for the entire dynamics simulation due to the evolving wave function density. I.e. convergence criteria will be revisited many times and it is therefore important each visit does not lead to addition of SPs unless really needed.