muse has 11 distinct synonyms spread across 1 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
in ancient Greek mythology any of 9 daughters of Zeus and Mnemosyne; protector of an art or science
the source of an artist's inspiration
“Euterpe was his muse”
reflect deeply on a subject
“I mulled over the events of the afternoon”
Synonyms, antonyms and the broader and narrower relations for muse come from Princeton University’s WordNet. Full sources and licences.