While Pino is busy packaging Krita 3.1.1 for Debian, you can easily run the latest Krita by getting the official appimages that I prepare myself. (Being the Krita maintainer and project lead.)
I also noticed that 3.1.1 is available on ubuntu snap. At this point I am not sure if I should go with snap or appimage. Either way, it is great to get packages directly from the developers!
Chrome has its own deb repository -- maybe more active projects need this too. (Maybe there's a service to be had hosting and configuring repos?)
I'm on Xubuntu 16.4 and I have 2.9.7 installed. I missed the entire year of developments. 16.10 has 2.9.11 released Feb 4th. 17.4 has 3.1.1 but won't be released for ~4 months. Maybe we should blame Ubuntu for 6 month release cycles, or me for not upgrading, but regardless of the cause, Krita users don't have the new version.
16.04 and onward can now have apps decoupled from the OS release for apps that provide snaps, like Krita does. `snap install krita` will get you 3.1.1.
Worked on 16.10 and I'll use this on 16.4 too.