I am using Linux Mint 12 KDE (based on Ubuntu 11.10). Full install on Zotac ZBOX Nano 10. Had zero sound from HDMI. Not sure which of these things fixed it, but it is working now.
1-Did ALL updates. No HDMI sound at this point.
2-Did search for proprietary drivers thru Applications/System//Extra Drivers.
3-Installed the first AMD Driver in the list. (2nd one did not work). Rebooted. Still no sound.
4-Unplugged HDMI from the ZBOX and replugged. Still no sound.
5-Opened Audio Mixer by clicking Speaker Icon(Volume control) in tray. Saw notification that Mint 12 thought there were several files (AMD DRIVERS) that it could ignore and asked for confirmation. I chose "NO".
6-In the Audio Mixer I selected "Settings", then in the Sound and Video Configuration Window I selected Device Preferences/Audio Playback/Music. In Rt. Side pane highlighted Internal Audio Digital Stereo(HDMI)
7-Pressed "Test" button- Viola! Sound! YAY!
8-With Internal Audio Digital Stereo(HDMI) still highlighted, pressed the "Prefer" button. This moved HDMI to the Top of the Device Preference list. Clicked on "Apply".
9-Opened up AMAROK and started listening to killer digital music on the Cool Streams "Darkerradio" Stream. Sweetness!
Hope this helps.