Save state to disk w/ VFIO PCI?

I managed to get VGA passthrough working on Ubuntu and it is awesome but something's missing - I wondered whether or not it would be possible to save the VM state to disk so that I can essentially pause games in my Windows VM and come straight back to them later.

That would really be quite something. I had a look around and there were mutterings from posts about a year ago that it wasn't doable but I wondered if any tracks had been made.