wither vs die down

wither and die down both are verbs.

Word	Noun	Adjective	Verb	Adverb
wither	No	No	Yes	No
die down	No	No	Yes	No

As verbs, die down is a hyponym of wither; that is, die down is a word with a more specific, narrower meaning than wither:

Other hyponyms of wither include atrophy, blast, die back, dry up, mummify.

wither (verb)	die down (verb)
wither, as with a loss of moisture	suffer from a disease that kills shoots
lose freshness, vigor, or vitality	become progressively weaker