In English, the word diet is most often used for simply describing which kind of food you eat. However, I think saying "I'm on a diet" can also mean you're (temporarily) targeting to reduce weight. (In German the similar word 'Diät' is almost exclusively used in the context of weight loss.) Does 'la dieta' usually imply a diet for losing weight or is it rather the general meaning?
I've come across estar a regimen to mean being on a diet (in a Spanish story book), but wordReference also suggests estar a dieta to mean being on a diet. I don't know if there are regional differences.
Also 'ponerse a regimen/dieta' o 'hacer regimen/dieta' would mean to follow a diet.
The article is not needed in the English translation. For example, La dieta puede controlar la diabetes. Translation: Diet can help control diabetes. One wouldn't say "the diet"?
Un plan nutritivo o en ingles: "A medically supervised nutrition plan". Otherwise, diet always means NO. 22Aug16