This is a super hacky-patchy-sketchy version of how far I've gotten with setting up Diffux on CircleCI.
We use Webpack that outputs a file like public/client/1.diffux.0198u2j129832hjf3.js or something so I copy it to ./diffux-old.js and ./diffux-new.js. I also have two yaml files for both runs -- it would be great if we can instead just pass those files as command line options to Diffux. There's also a bug in Diffux, see a comment in circle.yml.
Also, the first couple of lines of circle.yml are not super relevant but I kept them in there as it was stuff I ran into in the last few months so figured it might be useful for you too.