The rise of self-driving cars (SDCs) presents important safety challenges to address in dynamic environments. While field testing is essential, current methods lack diversity in assessing critical SDC scenarios. Prior research introduced simulation-based testing for SDCs, with Frenetic, a test generation approach based on Frenet space encoding, achieving a relatively high percentage of valid tests (approximately 50%) characterized by naturally smooth curves. The "minimal out-of-bound distance" is often taken as a fitness function, which we argue to be a sub-optimal metric. Instead, we show that the likelihood of leading to an out-of-bound condition can be learned by the deep-learning vanilla transformer model. We combine this "inherently learned metric" with a genetic algorithm, which has been shown to produce a high diversity of tests. To validate our approach, we conducted a large-scale empirical evaluation on a dataset comprising over 1,174 simulated test cases created to challenge the SDCs behavior. Our investigation revealed that our approach demonstrates a substantial reduction in generating non-valid test cases, increased diversity, and high accuracy in identifying safety violations during SDC test execution.