I think about using mvvmFX framework for JavaFX but I don't understand if it supports CDI. In wiki page about CDI is not ready. Could anyone say?
mvvmFX supports CDI. There is a separate module for CDI that you should include in your project. Some basic informations about using dependency injection in general with mvvmFX and with CDI can be found in the wiki here.
There is also an example application using CDI available in the repository.