There is a Linux-first clone of Paint.net called Pinta[1], but development stalled a few years ago[2] and the lead developer was asking for contributions to the codebase as of six months ago[3]. It has since been pulled from several distros' repositories, though it can of course still be built from source. It was a fantastic alternative to Paint.net when it was in development, but the last official release was quite buggy. Thankfully, work has resumed on it[4] and hopefully it will have another stable release soon.
On the other side, I can say that Krita has definitely improved over the years; it's stable enough now for me to use at work as a Photoshop alternative on Windows (though I still do most light editing in Paint.net).