Cards are discarded in a Magic game only from a player's hand. Effects that put cards into a player's graveyard from anywhere else do not cause those cards to be discarded.
Archfiend of Spite
If you choose not to cast a card with madness when the madness triggered ability resolves, it's put into your graveyard. Madness doesn't give you another chance to cast it later.
Madness works independently of why you're discarding the card. You could discard it to pay a cost, because a spell or ability tells you to, or because you have too many cards in your hand during your cleanup step. You can't discard a card with madness just because you want to, though.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Tomasz Jedruszek
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
