The only study I'm aware of is the following:
Cannabis increased verbal fluency in low creatives to the same level as that of high creatives. Cannabis increased state psychosis-like symptoms in both groups and the high creativity group were significantly higher in trait schizotypy, but this does not appear to be linked to the verbal fluency change. Acute cannabis use increases divergent thinking as indexed by verbal fluency in low creatives.
Regarding whether THC or CBD causes an increase in creativity the authors note that:
A few studies have attempted to objectively investigate whether cannabis increases creativity. Cannabis users produced more original (i.e. statistically infrequent) responses on an associative ability test when intoxicated with the drug compared to users given placebo (Block, Farinpour, & Braverman, 1992). Similarly, verbal fluency was significantly and dose-dependently improved by THC (the active ingredient in cannabis) compared with placebo in healthy volunteers given all treatments (Curran, Brignell, Fletcher, Middleton, & Henry, 2002). In contrast, Tinklenberg, Darley, Roth, Pferbhaum, and Koppel (1978) found that cannabis did not enhance scores in uniqueness, fluency, flexibility or elaboration during an object description task, considered to be a measure of creativity.
Schafer et al. 2012: Investigating the interaction between schizotypy, divergent thinking and cannabis use