Thinking on this has changed a lot in the last 20 years. Up until the early 90s it was pretty much taken for granted that any pictorial depiction of a mythological scene was a derivative work, based on an authoritative literary version of the myth. The pendulum has swung sharply away from this view now, but how far it has swung depends on who you ask. The older view was a result of modern scholars, who are used to working with texts, fetishising those texts and treating them as an authoritative canon; in reality of course there's no reason for doing so. The fact that texts are the backbone of the mythological canon for modern encyclopaedias of myth has nothing to do with their status for ancient Greek artists. The older view also neglected the fact that we've lost enormously more material, both literary and pictorial, than has been preserved.

A few readings that I'd recommend if you're doing research on the topic:

• Burgess, J. 2001. The Tradition of the Trojan War in Homer and the Epic Cycle. Johns Hopkins.
• Snodgrass, A. 1998. Homer and the Artists. Cambridge.
• Lowenstam, S. 1992. "The uses of vase-depictions in Homeric studies." Transactions of the American Philological Association 122: 165-98.
• Lowenstam, S. 2008. The Trojan War Tradition in Greek and Etruscan Art. Johns Hopkins.

The introduction to Lowenstam's 2008 book is probably the best single piece on the topic. The long and short of it is that it is now thought that poetry had either relatively little impact, possibly even no impact at all, on pictorial representations prior to about 520 BCE or thereabouts.

After that date, there's abundant clear evidence of pictorial representations that are derived directly from a literary work, especially Homer, and in the latter 5th century we see a lot of depictions based on Athenian tragedies as well. But for the earlier period it appears as though both poetry and the pictorial arts are drawing on mythological traditions that are at least semi-independent, if not wholly independent. Even after 520, pictorial adaptations of literary works are fairly loose for quite a while: painters often take their inspiration from a literary work rather than trying to copy it. In the late 400s, and certainly once you get to the Hellenistic period (after 323), it's possible to find painters and sculptors trying to be very faithful to their source material.

For early painters, Lowenstam (2008) takes a moderate posture, trying to cast them as drawing on literary traditions but thoroughly reimagining the material using their own traditions and "language". For my money, that's still way too conservative; I'd go with Burgess and Snodgrass: there's basically no indication that artists prior to 520 or thereabouts drew on literary works at all. But it's probably best for you to make up your own mind.

I'd be happy to go into a few selected examples if you like, though I'd just be repeating what's in the bibliography I've mentioned. Also I'm away from home at the moment so I might not be able to get back to you promptly :-)