Another approach to compiler fuzzing is blackbox differential fuzzing. Generate random valid programs and see if they do the same thing with different compiler settings, or even with two or more different compilers. This does mean you need to generate valid programs, which present challenges in languages with undefined or implementation-specific behaviors.

This is blackbox, so it doesn't allow one to start from nothing as a greybox fuzzer would.

Anyway, testing is not like programming in that different approaches are incompatible. Different testing approaches typically have different blind spots, so they complement each other.