Autonomous driving systems (ADS) have been an active area of research, with the potential to deliver significant benefits to society. However, before large-scale deployment on public roads, extensive testing is necessary to validate their functionality and safety under diverse driving conditions. Therefore, different testing approaches are required, and achieving effective and efficient testing of ADS remains an open challenge. Recently, generative AI has emerged as a powerful tool across many domains, and it is increasingly being applied to ADS testing due to its ability to interpret context, reason about complex tasks, and generate diverse outputs. To gain a deeper understanding of its role in ADS testing, we systematically analyzed 91 relevant studies and synthesized their findings into six major application categories, primarily centered on scenario-based testing of ADS. We also reviewed their effectiveness and compiled a wide range of datasets, simulators, ADS, metrics, and benchmarks used for evaluation, while identifying 27 limitations. This survey provides an overview and practical insights into the use of generative AI for testing ADS, highlights existing challenges, and outlines directions for future research in this rapidly evolving field.