Is there a Vanilla JS replacement for the dialog widget provided by jQuery UI? It should at least allow to contain arbitrary markup, so alert or prompt are not an option.
Only to a certain extend. You might use alert, prompt or confirm dialogs (implemented as functions on the window object), but they can't be styled and look different between various browsers.
Creating a special modal/dialog with vanilla JS is of course possible. How hard it is depends on the features you want/need it to have.