Personal pet peeve - First of all, you can't target a body part with a diet. So "abs diet"? riiiight. Second, healthy food is not expensive. Provided you use common sense, and know how to substitute.
This is my torso, after losing 70 pounds, at age 45. (Actually, between age 43 and now) I did this on around $20 a week, total food cost. Lots of oatmeal, canned or dried fruit (fresh bananas are dirt cheap) soup, and the cheapest forms of protein I could find. Oh, and root vegetables. Lots and lots of dirt cheap root vegetables. My resting heart rate is 39, my BP is 114/52 and my cholesterol, while between 180 and 211, is off the charts on the good side, when adjusted for HDL/LDL.
Much ado is made in the fitness community about nutrients. I think, based on my own experience, the fascination with over-nutrifying is a bit wacked. Of course, I only have my own experience, losing a ton of weight, getting in terrific shape, and rolling back my physical clock 20 years; I guess I don't have a book, a TV show and a fitness magazine article to rely upon....
Most people overthink nutrition. Exercise more, eat less usually works. If you feel fatigue or have cravings, find the source of the missing nutrient that you can afford.
I have a co-worker that spends a fortune on supplements/******* constantly about the food selection/exercize equipment here.
One of us continues to get results; the other doesn't. Who do you suppose gets the results? "Hint - that would be me."