I don't have a diagnosis of anxiety. I have been diagnosed with major depression in the past when I was on a low fat, low protein vegetarian diet. I had a suicide plan and everything. I took anti-depressants for a while but stopped them several years ago.
Even though I was no longer taking medication and didn't think of myself as depressed, I now feel infinitely better about everything. Better than before and better than any time in my life. I feel sunny, confident, happy, radiant. It's just amazing.
I will share that I have two friends who went on a different diet from a 12-step program that defines abstinence as no flour (from any kind of grain, but real whole grains are fine) and no sugar. Both friends experienced profound mood effects. One of them took anti-depressants and no longer needs them. One of those friends spent the summer traveling and met some other people along the way who had done similar things--paleo diet, more fat and less grains, that sort of thing--and had similar results. The thing that astounds all of us the most is the huge change in our mental health. It's astonishing, really.
Female, 5'3", 50, Max squat: 202.5lbs. Max deadlift: 225 x 3.