Displays can now be driven over HDMI with this open-source VIA KMS/DRM driver that's largely developed by just James Simmons of the Linux kernel community.
Simmons published the initial VIA HDMI support to his DRM kernel Git tree yesterday. "Initial support for HDMI. Currently DVI monitor attached to a HDMI port is not supported nor is audio not implemented. A mode can be set but I see problems with setting the proper resolution. Will be addressed in a latter patch."
Shortly thereafter was another commit for tidying up HDMI support for VIA. "The rest of the changes needed to make HDMI work properly."
There's still no word on when the VIA kernel mode-setting driver may be proposed for inclusion into the mainline Linux kernel. For more details on the state and history, see VIA Kernel Mode-Setting Still Being Toyed With.