Creativity is a cornerstone of human evolution and is typically defined as the multifaceted ability to produce novel and useful artifacts. Although much research has focused on divergent thinking, growing evidence underscores the importance of perceptual processing in fostering creativity, particularly through perceptual flexibility. The present work aims to offer a framework that relates creativity to perception, showing how sensory affordances, especially in ambiguous stimuli, can contribute to the generation of novel ideas. In doing so, we contextualize the phenomenon of pareidolia, which involves seeing familiar patterns in noisy or ambiguous stimuli, as a key perceptual mechanism of idea generation--one of the central stages of the creative process. We introduce "divergent perception" to describe the process by which individuals actively engage with the perceptual affordances provided by ambiguous sensory information, and illustrate how this concept could account for the heightened creativity observed in psychedelic and psychotic states. Moreover, we explore how divergent perception relates to cognitive mechanisms crucial in creative thinking, particularly focusing on the role of attention. Finally, we discuss future paths for the exploration of divergent perception, including targeted manipulation of stimulus characteristics and the investigation of the intricate interplay between bottom-up and top-down cognitive processes.