Although diet has not been heralded as a form of treatment, it is certainly intuitive that it would play a significant role in depression. Interestingly the very things you crave may exacerbate your depression. This article has an interesting comparison of a change in diet versus social change, and their role in depression.
Needless to say depression and sleep are intertwined, and that diet would influence both makes total sense. However, the conclusions may surprise you.