Diet is essential to managing depression. The reason for that is everyone has a diet, you have to eat something! Unlike other things that may help depression, the right diet relieves depression but the wrong diet actually causes depression. So you get a big double wammy from the wrong diet because you are missing out on the anti-depression benefits as well as actively adding to your depression.
Considering how important diet is to depression there actually isn’t much research on it. The reason for this is because cash is king. Pharmaceutical companies are willing to invest big money in running studies for their drugs as they stand to make a lot of money from it. But no one stands to make much money from proving how great salad is or even multivitamins. However more research is starting to be done and so far the results look great.