Generative AI (GenAI) has achieved remarkable success across a range of domains, but its capabilities remain constrained to statistical models of finite training sets and learning based on local gradient signals. This often results in artifacts that are more derivative than genuinely generative. In contrast, Evolutionary Computation (EC) offers a search-driven pathway to greater diversity and creativity, expanding generative capabilities by exploring uncharted solution spaces beyond the limits of available data. This work establishes a fundamental connection between EC and GenAI, redefining EC as Natural Generative AI (NatGenAI) -- a generative paradigm governed by exploratory search under natural selection. We demonstrate that classical EC with parent-centric operators mirrors conventional GenAI, while disruptive operators enable structured evolutionary leaps, often within just a few generations, to generate out-of-distribution artifacts. Moreover, the methods of evolutionary multitasking provide an unparalleled means of integrating disruptive EC (with cross-domain recombination of evolved features) and moderated selection mechanisms (allowing novel solutions to survive), thereby fostering sustained innovation. By reframing EC as NatGenAI, we emphasize structured disruption and selection pressure moderation as essential drivers of creativity. This perspective extends the generative paradigm beyond conventional boundaries and positions EC as crucial to advancing exploratory design, innovation, scientific discovery, and open-ended generation in the GenAI era.