Dutch roll tends to happen when the lateral stability is greater than the directional stability - the rolling out of the sideslip force is stronger than the tendency for the aircraft to yaw towards the sideslip. So divergence in roll to the right=sideslip right. Sideslip right=roll left due to dihedral and/or sweep. Roll left=increased drag on upgoing (right) wing due to inc lift dependent drag = yaw right ie roll and yaw opposite.
If directional stabilty is higher than lateral, as usually in light/straight wing aircraft then same sideslip right=yaw right (outweighing any tendency to roll back to the left) so right yaw=right roll etc and you have a spiral dive.