Since Arcanist lets you cast a card without paying its mana cost, is it possible to cast Dig Up with Cleave? With cleave worded as "you may cast this spell for its cleave cost, If you do...", it makes me think that casting it for free wouldn't allow you to use the alternate cost, but I'm not sure since they noted in the preview that the CMCMana Value is 1 regardless of if you cast it with Cleave.
Cleave expresses an alternative cost (C.R. 702.148a), so you can't choose to cast Dig Up with Dreadhorde Arcanist for its cleave cost, since no two alternative costs can be applied to the same spell (C.R. 118.9, 118.9a).
Note, however, that a spell's mana value is determined regardless of what was spent to cast the spell or whether its mana cost or an alternative cost was paid for the spell (C.R. 202.3). The only thing that can change a spell's mana value is the value of X for the spell, and then only if the spell has X in its mana cost (C.R. 202.3e). See also this thread.
EDIT (Dec. 22): Edited since the rules for Innistrad: Crimson Vow were released.