'nut-infused' originates from Modern English as a compound of 'nut' and the past-participle form of 'infuse.' 'Nut' comes from Old English 'hnutu' meaning an edible seed, and 'infuse' ultimately comes from Latin 'infundere' (via Old French 'infuser'), where 'in-' meant 'into' and 'fundere' meant 'to pour.'

'infuse' changed from Latin 'infundere' to Old French 'infuser' and then entered Middle/Modern English as 'infuse' (meaning to pour in or to steep). The compound 'nut-infused' is a modern English formation combining 'nut' + 'infused' to describe something permeated by nuts or nut flavor.

Initially, 'infuse' meant 'to pour into' (literally). Over time it evolved to mean 'to steep, permeate, or impart flavor/qualities into' something. Thus 'nut-infused' now means 'permeated or flavored with nuts' rather than a literal pouring of nuts.