Empathy research has long emphasized accuracy when imagining other minds. We explore whether empathy can be a creative process, where people think of multiple diverging possibilities of others' experiences. We developed two tasks to measure creative empathy. First, we adapted "forward flow" to measure the dynamic unfolding of creativity while imagining other minds, quantified as semantic distance between mental state concepts when freely associating the contents of other minds. Second, we developed a divergent thinking task where participants reflect on others' mental states and responses are scored using subjective and automated methods. In Studies 1-3, participants instructed to "be creative" showed higher scores than those instructed to be accurate and a no-instruction control, demonstrating that people vary in how creatively they approach empathy. In Study 4, participants instructed to be empathic (vs. objective) toward a target showed greater creativity on the divergent thinking task, demonstrating that empathy can produce creativity. Creativity on these tasks were inconsistently associated with trait and state empathy measures, suggesting complex relationships between creative empathy and empathic outcomes. Overall, these findings support a novel approach to measuring empathy that accounts for creative processes, broadening the scope of empathy and creativity research.