Is it possible to naturally heal cavities by changing diet? or is there any other way to naturally heal the cavities?

That depends on what: You mean by "a cavity". If you mean an area of decalcified enamel that has not yet developed into a hole or a sticky area, than yes, you may be able to heal the area with proper Fluoride therapy. If you mean a sticky hole, then No, it is too late, you can not heal this and it must be restored by a dentist to stop progression. See your dentist for an evaluation.

See your dentist: Tooth decay is the world's most common health problem. Cavities are permanently damaged biological structures caused by bacteria, acid and other factors. If cavities aren't treated, they get larger and more complicate treatment is necessary. See a dentist for professional consultation, x-rays and treatment. Good luck.

Natural Healing: Do you mean treatment to restore decayed teeth without the intervention of a dentist? If so, the answer is no. You'll need a dentist to evaluate the teeth and treat them.

Not possible: The short answer is no. A cavity can only be filled, a cavity will not heal by regenerating itself , we have no way as of today to heal cavities, may be in the future...