Possession by a spirit or similar entity — when a spirit takes hold of a person or object (often used in religious, folkloric, or horror contexts).
その村では、憑依を祓うための儀式が今も行われている。
In that village, rituals to exorcise possession are still performed.
ホラー映画では、主人公が悪霊に憑依される場面が多い。
In horror films, there are often scenes where the protagonist becomes possessed by an evil spirit.
彼女は『アイデアに憑依されたように』絵を描き続けた。（比喩的用法）
She kept painting as if possessed by an idea. (figurative use)
Dependence on something — a more formal or literary sense indicating being heavily dependent (sometimes used figuratively).
彼の判断は特定の理論への憑依に近く、客観性を欠いていると批判された。
His judgment was criticized for being almost a dependence on a particular theory, lacking objectivity.
その作家はある思想への憑依から抜け出せず、作品に偏りが見られる。
The writer could not free himself from dependence on a certain ideology, and his works show bias.