Divergent thinking activities, like research and ideation, are key drivers of innovation in UI/UX design. Existing research has explored AI's role in automating design tasks, but leaves a critical gap in understanding how AI specifically influences divergent thinking. To address this, we conducted interviews with 19 professional UI/UX designers, examining their use and perception of AI in these creative activities. We found that in this context, participants valued AI tools that offer greater control over ideation, facilitate collaboration, enhance efficiency to liberate creativity, and align with their visual habits. Our results indicated four key roles AI plays in supporting divergent thinking: aiding research, kick-starting creativity, generating design alternatives, and facilitating prototype exploration. Through this study, we provide insights into the evolving role of AI in the less-investigated area of divergent thinking in UI/UX design, offering recommendations for future AI tools that better support design innovation.