Both Ubuntu and Fedora have made it official: support is coming soon for running local generative AI instances.
An epic and still-growing thread in the Fedora forums states one of the goals for the next version: the Fedora AI Developer Desktop Objective. It is causing some discontent, and at least one Fedora contributor, SUSE’s Fernando Mancera, has resigned.



Debian or anything based directly on it
Debian can also run AI models. Pretty dumb reason to get mad about.
Every linux distro can run AI models, there is 0 reason to support distros that ship with AI bullshit by default