Creatures assign the same amount of combat damage as though Gratuitous Violence weren't on the battlefield. Gratuitous Violence doubles certain combat damage when it would be dealt, so after it's assigned (C.R. 510.1, 510.2).
Gratuitous Violence's ability doesn't change how combat damage is assigned (as trample does [C.R. 702.19]); effects that would affect the damage a creature would deal, as with Gratuitous Violence's ability, don't change the amount of combat damage creatures assign (C.R. 510.1c-d apply generally and C.R. 702.19b applies to trample). Therefore, creatures assign combat damage without regard to those effects.
Example: 4/4 attacking (with x2 damage from [card]Gratuitous Violence[\card]) blocked by a 5/3.
How much gets assigned to the creature & player (with minimum lethal damage to the blocker)?
Gratuitous Violence's ability doesn't change how combat damage is assigned (as trample does [C.R. 702.19]); effects that would affect the damage a creature would deal, as with Gratuitous Violence's ability, don't change the amount of combat damage creatures assign (C.R. 510.1c-d apply generally and C.R. 702.19b applies to trample). Therefore, creatures assign combat damage without regard to those effects.
Questions like yours tend to arise whenever trample as well as another effect that affects how combat damage is dealt are involved (examples include Calamity Bearer; Torbran, Thane of Red Fell; Insult; protection abilities [C.R. 702.16, especially C.R. 702.16e]; Kor Chant; Opal-Eye, Konda's Yojimbo; Gisela, Blade of Goldnight; and so on).
See also this submission (Vorinclex, Monstrous Raider), this thread (Insult), and this thread (Kor Chant).