The "standard" definition of creativity as novel and useful describes creative products, but creativity is constituted by processes. This misalignment contributes to the oft-noted challenges of operationalizing creativity. Here, we distinguish creativity as a process from creativity as an attribute (i.e. "creative-ness"). Operating from "a priori" premises of creativity theory, we develop a process definition of creativity. Specifically, creativity is defined as internal attention constrained by a generative goal. This definition comprises three criteria: (1) attention is directed internally (toward mental representations); (2) attentional operations (e.g. search, manipulation) are constrained to fit parameters of a to-be-achieved goal state (whether or not a goal is actually achieved); and (3) the goal state is generative (not already precisely held in memory). We illustrate how these three definitional process elements align with insights yielded by creativity neuroscience, clarify ontological distinctions (e.g. from mind-wandering and retrieval), and relate the process definition to process-based models. The process definition provides minimal necessity and sufficiency criteria for whether a process should be considered creativity, but does not exclude the many other perceptual, emotional, etc. elements that can contribute to creativity processes. Researchers should specify whether they are studying creativity-as-process vs. "creative-ness," and consider including process-focused assessments.