Designing public spaces requires balancing the interests of diverse stakeholders within a constrained physical and institutional space. Designers usually approach these problems through participatory methods but struggle to incorporate diverse perspectives into design outputs. The growing capabilities of image-generative artificial intelligence (IGAI) could support participatory design. Prior work in leveraging IGAI's capabilities in design has focused on augmenting the experience and performance of individual creators. We study how IGAI could facilitate participatory processes when designing public spaces, a complex collaborative task. We conducted workshops and IGAI-mediated interviews in a real-world participatory process to upgrade a park in Los Angeles. We found (1) a shift from focusing on accuracy to fostering richer conversations as the desirable outcome of adopting IGAI in participatory design, (2) that IGAI promoted more space-aware conversations, and (3) that IGAI-mediated conversations are subject to the abilities of the facilitators in managing the interaction between themselves, the AI, and stakeholders. We contribute by discussing practical implications for using IGAI in participatory design, including success metrics, relevant skills, and asymmetries between designers and stakeholders. We finish by proposing a series of open research questions.