I'm on a diet, I'd prefer not to come to dinner.
'Dieta' — DI-e-ta. Three syllables, stress on the first. Don't merge the vowels.
Use specifically for food-related social events when dieting. In Italy this will generate debate — Italians may try to convince you to come anyway and eat little, so be prepared.
'Sono a dieta' is the standard Italian phrase for being on a diet. Declining a dinner invitation for diet reasons is unusual in Italy — food is communal and refusing to participate in a meal is almost culturally offensive to the host.
Sto cercando di mangiare sano.
I'm trying to eat healthily.
Softer than 'dieta' — implies lifestyle change rather than restriction
Ho delle restrizioni alimentari.
I have dietary restrictions.
Formal — used for medical or allergy-related restrictions
Il medico mi ha detto di stare attento/a con il cibo.
The doctor told me to be careful with food.
Medical authority removes all debate — no Italian will argue with a doctor
Declining an Italian dinner invitation for diet reasons is viewed as almost antisocial. Hosts take food refusal personally. A more Italian approach is to come, eat modestly, and make strategic conversation — skipping entirely is a last resort.