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We investigate the scaling limit of the seed bank diffusion when reproductionand migration (to and from the seed bank) happen on different time-scales. Moreprecisely, we consider the case when migration is `slow' and reproduction is`standard' (in the original time-scale) and then switch to a new, acceleratedtime-scale, where migration is `standard' and reproduction is `fast'. This ismotivated by models for bacterial dormancy, where periods of quiescence can beorders of magnitude larger than reproductive times, and where it is expected tofind non-trivial degenerate genealogies on the evolutionary time-scale.  However, the above scaling regime is not only interesting from a biologicalperspective, but also from a mathematical point of view, since it provides aprototypical example where the expected scaling limit of a continuous diffusionshould (and will be) a jump-diffusion. For this situation, standard convergenceresults often seem to fail in multiple ways. For example, since the set ofcontinuous paths from a closed subset of the c\`adl\`ag paths in each of theclassical Skorohod topologies $J_1, J_2, M_1$ and $M_2$, none of them can beemployed for tightness on path-space. Further, a na\"ive direct rescaling ofthe Markov generator corresponding to the continuous diffusion immediatelyleads to a blow-up of the diffusion coefficient. Still, one can identify awell-defined limit via duality in a surprisingly non-technical way. Indeed, weshow that a certain duality relation is in some sense stable under passage tothe limit and allows an identification of the limit, avoiding alltechnicalities related to the blow-up in the classical generator. The resultthen boils down to a convergence criterion for time-continuous Markov chains ina separation of time-scales regime, which is of independent interest.

Separation of time-scales for the seed bank diffusion and its jump-diffusion limit