Yes, It's directly related to diet, though genetics does play a small part. I've experimented in the past with this subject. I had a control colony of roughly 40-60 individuals, (mostly young nymphs) fed a diet of only dry cat food. In the other colony of roughly the same population, they were fed dry dog food with bright-colored fruits. I.e. oranges and red apples. When the control population came to be mostly adults, the group color was sort of a dark brown. And in the other tank the adult colorations were all eye-catching oranges and dark reds. Exactly how the color of food represents itself through the final color scheme of an adult cockroach, I haven't the slightest idea.
Perhaps less fruit/veggies and more brown-ish pet food would accomplish this? Some individuals from both tanks had vaired colors, so diet isn't 100% influential, I guess.