In this paper we consider the problem of gossiping in a network to diffuse the average of a sub-set of nodes, called sources, and directing it to another sub-set of nodes in the network called destinations. This case generalizes the typical average consensus gossiping policy, where all nodes are both sources and destinations. We first describe prior results we obtained on a static network topology and gossip policy, highlighting what conditions lead to the desired information flow. We show that, through semi-directed flows, this formulation allows to solve the problem with lower complexity than using plain gossiping policies. Inspired by these results, we move on to design algorithms to solve the problem in the dynamic case. For the dynamic network scenario we derive conditions under which the network converges to the desired result in the limit. We also provide policies that trade-off accuracy with increased mixing speed for the dynamic asymmetric diffusion problem.