I think it's possible to become addicted to something without having first been depressed, so no, I don't think depression is a prerequisite for addiction. But the two do have an association that makes it likely for them to co-occur, and scientists are still trying to figure out what that is. Many people who are depressed self-medicate with substance abuse or other addictive behaviors like eating disorders, so it's not surprising that depression can lead to addiction problems. On the other hand, addiction places a lot of stress on relationships, health, and most other aspects of life, so it also makes sense that one of the consequences of addiction might be depression.
It's not an entirely clear relationship and depression and addiction often occur together, but I think it's safe to say that a person can become an addict without first being depressed.
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