Consider a general wireless network with multiple source-sink pairs, with each source intending to communicate independent information to its destination. In this work, we characterize the capacity of this multiple-unicast traffic model for a general wireless network to within a multiplicative logarithmic factor in the number of source-destination pairs. This is a worst-case gap, and therefore holds for *every* instance of a wireless network specified by a connectivity graph. We also demonstrate a sharper factor $4$ gap for the sum-rate of general X-networks. These results are proved by generalizing the approximate max-flow min-cut characterization for multiple unicast in undirected graphs by Leighton and Rao to "polymatroidal" networks, which have interacting capacities.