I used a HDMI cable with a DVI adapter without issue, but I started having issues when I ditched the adapter. The resolution went down, and the smaller image was centered, leaving a big black border.
So how did I fix it? Uncomment or add the following line to /boot/config.txt
Value 2 means normal HDMI (sound will be sent over HDMI if enabled). Value 1 would be DVI mode. No idea why the adapter made it work perfectly without the settings change. Autoconfig?
I think it's amazing that the Raspberry Pi can handle 1080p.