It is very difficult to protect others from copying the style of human artists, as copyright law covers specific works of art, not general styles, methods, or genres. You can have trademark rights in style if it is part of your unique brand, but only if most consumers would associate it with you as a commercial artist by name and the GenAI outputs create confusion in the marketplace as to who made which works of art. And while you do have rights to control your image, name, and identity under your “right of publicity,” those are generally limited to exploitation of your personhood and not the works you create in the world. Deepfakes, on the other hand, might run afoul of right of publicity laws if they commercially exploit your image, voice, or other aspects of your identity.