We layout a network infrastructure that leverages the storage and computing power of a cloud residing in the core for collecting network status and computing multi-path scalable video coding (SVC) streaming provisioning strategies. Therefore, in addition to its conventional tasks in the application layer, the cloud also gets involved in the network layer for the optimization of routing and forwarding. We call this scheme as cloud-assisted SVC streaming, and use it to further improve the performance of SVC streaming by using close cooperation between cloud and network. Compared to source-routing based provisioning, the cloud-assisted scheme can provide more cost-effective provisioning strategies by utilizing better knowledge of network environment together with more powerful computation power. We then propose several multi-path provisioning algorithms for cloud-assisted SVC streaming in heterogeneous networks. To the best of our knowledge, these are the first proposals to work on the problem of adaptive multi-path SVC streaming under the bandwidth, delay and differential delay constraints. Our design of the provisioning algorithms starts from an approach that is based on Max Flow and an Auxiliary Graph. Several extensions are then made based on this approach to address the situations such as provisioning from multiple sources and provisioning in dynamic network environments with rapid background traffic fluctuations. Simulations in both static and dynamic network environments show that the proposed algorithms can achieve effective performance improvements in terms of request blocking probability, bandwidth utilization, packet delay, packet loss rate, and video playback quality.