A system for sender-driven video streaming from multiple servers to a single receiver is considered in this paper. The receiver monitors incoming packets on each network path and returns, to the senders, estimates of the available bandwidth on all the network paths. The senders in turn employ this information to compute transmission schedules for packets belonging to the video stream sent to the receiver. An optimization framework is proposed that enables the senders to compute their transmission schedules in a distributed way, and yet to dynamically coordinate them over time such that the resulting video quality at the receiver is maximized. Experimental results demonstrate that the proposed streaming framework provides superior performance over distortion-agnostic transmission schemes that perform proportional packet scheduling based only on the available network bandwidths.