My face is gaunt. I have a good diet and lifestyle, and I don't want to get surgery. What can I do?

You need volume . Fat transfer or sculptra is a great way to get volume back in the face to rejuvenate and help give back a more youthful appearance.
Fillers. There are many options to replace facial volume- from fillers like Radiesse (dermal fillers) and sculptra- to fat transfer.
What's the reason? The reason for the appearance will dictate your options. If you are significantly underweight, simple weight gain can eliminate the gaunt look. Injectable material might help improve it, or surgery may be the only option. If it is, then you'll have to age gracefully!
Fillers. Fillers may provide a temporary correction to the loss of volume.
Fat Injections. Fat injections to the face are a great way to restore volume. As we age, our dermis thins. Fat injections put volume back. This is performed by removing a small amount of adipose fat from your stomach or flanks, processing the fat, and then re-injecting the high density fat into your face with very fine injections. I prefer this option to synthetic injectables because it is your own tissue.
Consider fillers. You may want to meet with a plastic surgicenter to discuss fillers or lipoinjection ( fat transfer).
Fat Transfer. Localized fat loss is associated with aging and can lead to deflation and loss of youthful volume, proportion and shape. Fat transfer procedures, reinjecting extracted fat, are one effective non-surgical method of correcting volume loss. They involve only local anesthesia, little bruising, swelling or discomfort, and minimal recovery time. Injectable fillers may also be an effective solution.
Fat vs Fillers. You need volume. Either fillers, fat grafts. implants. Since you don't want surgery, fat transfer better than fillers since more permanent. See facial plastic surgeon for evaluatoin.