Opinion:
Same method, but use a data series (e.g. like the Theories class). That way, everything is detailed so the user can see what the tested dataset is, without having to read the entire test case. Effectively an iterator on a test function.
See functional-test/src/test/java/org/zanata/feature/account/InvalidEmailAddressTest.java for example.
I may have misinterpreted what is meant by generator, but for anything that is created "on the fly" it needs to be a separate test suite for fuzzy testing.