In the book Odyssey, it's said that ambrosia was carried to Olympus by doves :
Here not even a bird may pass, no, not even the timid doves that bring ambrosia to Father Jove, but the sheer rock always carries off one of them, and Father Jove has to send another to make up their number
Also, Demeter was considered the goddess of crops and agriculture, being intrinsically linked to food.
The Roman goddess counterpart is Ceres. 
Ceraon, Deipneo and Matton are greek semi-gods related to food. More specifically the bread preparation stages.
To Romans, Abundantia was the personification of abundance, carring the Cornucopia - presented as a large horn-shaped container overflowing with produce, flowers, or nuts 
 HOMER. The Odyssey. 1:Translated by Samuel Butler. p. 202.
 FINLEY, M. I.. The World of Odysseus. 4. ed. New York: New Yorknyrb Classics, 2002.
 Apollodorus. The Library of Greek Mythology. 1. ed. Oxford University Press, 2008.
 PARKER, R. Polytheism and Society at Athens. OUP Oxford, 2005.