Sure... but not safely, nor permanently. A "crash diet" and/or strenuous exercise plan can slim down the body - face included - mostly because it will deplete the body of water, and some fat. As well, this can happen without intention - for example, when a person is under continued stress, and not eating enough as a result. The combination of increased and nearly constant adrenaline production, and lowered caloric intake, can make the body lose weight very quickly. And yes, it can affect the appearance of the person's face. Neither of the above is recommended as a way of doing so, however. It depends on your body. I will say (and I'm sure there are critics out there) that my mother , sister, and myself put ourselves on the Atkins diet a month before my sisters wedding. We lost considerable weight in the first 2 weeks. I cheated but my sister lost 25 pounds before her wedding. I will also admit that it was mostly water weight the first 2 weeks. NO, you cannot lose weight in any one place. When you lose weight, it is all over your body. Anyone who tells you you can lose weight in one spot is trying to sell you something, or is just ignorant. The only way to lose weight in one spot is with liopsuction.