Fibroids,can they be shrunk naturally.If so how does diet contribute to that process?

Not really, and not much.

You're body has its own, natural way of dealing with them. When this mechanism breaks down, then fibroids form. They don't often go away on their own.

A healthy, balanced diet is always a good idea. However, there is not a good or specific diet for fibroids. Sorry for the bad news.

Less caffeine and fewer sugary foods will help to reduce fibroids, so I hear.
According to one of my reference books you should do the following:
Avoid eating cabbage, beets, rutabaga, soy beans, spinach and turnips.
Take some form of aerobic excercise.
Eat potatoes, apples and sesame seeds in order to stimulate the thyroid gland.
Supplements that can help include kelp(150mcg 3 times a day, Tyrosine (500mg 4 times a day and vitamin B1 (100mg 3 times a day.
Avoid the following foods:
legumes, oats, alfalfa, sunflower seeds, endive, wheat germ, brewer's yeast and liver.
Anumber of other supplements and herbs are also recommended including 100mg B complex that does not contain PABA or folic acis, B6, 100mg 3 times a day, lipotropic factor, 1000mg 2 times a day, vitamin E 100IU once a day, red clover combination 2 tablets 3 times a day 1 milk thistle tablet 3 times a day, red rasberry helps prevent bleeding, queen of the meadow helps reduce pain and false unicorn corrects many problems of the reproductive system. Sorry there is so much of it, but that's what the man says.
Good luck
How to Stay Out of the Doctor's Office by Dr Edward M Wagner and Sylvia Goldfarb