Nethog is a tool similar to top which will show you some useful tabular information on network activity for a given interface including relevant process / PID.
sudo nethog <interface>
Output behaves like top (updates regularly) and looks kind of like this:
NetHogs version 0.8.0 PID USER PROGRAM DEV SENT RECEIVED 2633 username /home/username/.dropbox-dist/dropbox wlan0 0.070 0.061 KB/sec 5752 username /opt/google/chrome/chrome wlan0 0.026 0.033 KB/sec ? root unknown TCP 0.000 0.000 KB/sec TOTAL 0.096 0.094 KB/sec