This clinical trial aims at assessing whether consumption of olive pomace oil in the diet may benefit persons with type 2 diabetes mellitus or persons at risk of developing the disease (prediabetic persons). The main questions the study aims to answer are: * May olive pomace oil prevent a high increase of blood glucose levels when consumed in a meal together with carbohydrates in diabetic/prediabetic patients? * May olive pomace oil decrease fasting blood glucose levels of diabetic/prediabetic patients after consuming it daily? * May daily consumption of olive pomace oil improve glucose homeostasis and other alterations like elevated blood lipids or inflammation, which also affect persons with diabetes or prediabetes? Researchers will compare the effect of consuming olive pomace oil to the effects of a comparison oil (high-oleic acid sunflower oil). Participants will: In different days, they will consume white bread alone or the oils (olive pomace oil, high-oleic acid sunflower oil or extra virgin olive oil) spread on white bread and blood will be collected at different times during 2 h. This study to observe the increase of blood glucose after a carbohydrate-rich breakfast will be part of the so-called postprandial study, and will be conducted during 3 weeks, during which participants will consume corn oil on a daily basis. Participants will also take part in the chronic study, that will last 22 weeks in total. During this study, they will firstly wash the effects of the oil they normally consume in their diets by consuming corn oil during 3 weeks. It is during these weeks when they will attend the Human Nutrition Unit (HNU) of ICTAN to carry on the postprandial study described in the previous paragraph. After the initial 3 weeks, participants will consume olive pomace oil as the only oil in their diets during 8 weeks, wash its effects again by consuming corn oil during 3 weeks and then change to consume the other oil (high-oleic acid sunflower oil) during 8 weeks. During the chronic study, they will visit the clinic once every 4 weeks for checkups and tests. They will refrain from eating other oils or specific fat-rich foods. Participants will also attend our phone calls to ask them what they ate the day before on different weeks during the study, and wear an accelerometer during 1 week to record their physical activity. They will keep a diary of the doses of insulin/metformin used and the blood glucose levels they measured at home.