I will have thoughts originate with no known cause (no direct correlation to the current activity nor dialogue taking place in my mind) that at times can border on genius.

inspiration (n.)

c. 1300, "immediate influence of God or a god," especially that under which the holy books were written, from Old French inspiracion "inhaling, breathing in; inspiration" (13c.), from Late Latin inspirationem (nominative inspiratio), noun of action from past-participle stem of Latin inspirare "blow into, breathe upon," figuratively "inspire, excite, inflame," from in- "in" (from PIE root *en "in") + spirare "to breathe" (see spirit (n.)). ,

And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. [Genesis ii.7]

The sense evolution seems to be from "breathe into" to "infuse animation or influence," thus "affect, rouse, guide or control," especially by divine influence. Inspire (v.) in Middle English also was used to mean "breath or put life or spirit into the human body; impart reason to a human soul." Literal sense "act of inhaling" attested in English from 1560s. Meaning "one who inspires others" is attested by 1867. *

It's beyond my understanding what force is breathing life into either scenario.