Willpower won't do it, because that is tantamount to ignoring your body's signals, like ignoring your feeling of hunger or ignoring that you crave food. You don't sustain that; you just have to work with your body. Your body and your mind have to be on the same wavelength, then it will work. So you have to make sure that craving is no longer there.
The only way to get rid of that gnawing feeling is to really nourish your body so that it is truly satiated. And you don't do that by eating less, but by eating more quality food, so that your hormones calm down, so that your body can send the right signals to your brain, signals that say, "I've had enough. And suddenly you find that you no longer crave that piece of cake at all, that you now manage to stay away from that bread, that you can leave the chips untouched.
So it has little to do with willpower, but simply with your body being truly satiated. When you eat natural foods, your body functions better. Many insist on behavior change, but you can't sustain that behavior change if it makes you constantly hungry and unhappy. Therefore, my angle is: eat differently and you will see that your behavior will change.