Rebirth does not necessarily imply the existence of Atma.

For Vedic people, an individual is a combination of body and soul. The body keeps changing during the lifetime of an individual. But the soul remains unchanged. And it is this soul that migrates from the dying body to a newly formed body in the womb of the next mother.

Buddhists have a rebirth theory that is quite different from the rebirth theory of the Vedic people. To understand that, you should first know how Buddhism looks at an individual.

Buddhists view an individual as a continuously changing sequence of bodies and minds. (Actually, each body/mind in the sequence replaces the previous one.). This sequence gives the impression of an individual, though there is no individual in the conventional sense. So, they don’t need the concept of soul. In fact, Buddhists deny the existence of any soul which is unchanging.

This sequence of body/mind keeps going till the death. At the last stage of this sequence, the contents of the last mind of the dying person (?) gets transferred to another newly formed mind in the womb of the next mother (which is associated with the fetus). From then on, another sequence of body/mind starts as another individual.

So, Buddhists don’t need to believe in soul, unlike the Vedic people.

The images are from Dr. King’s book “The Marvels of the Mind Part II - Missing dimensions in our current understanding of the mind”.