No one can pass down to others their personal sins. We say that the original sin of Adam and Eve is passed down through the generations, but original sin is not the actual fault of the recipient. Rather, its effect is the privation of grace and the loss of original innocence that our first parents had.
Likewise, one can pass the effects of one’s sins through generations. Let’s say that someone is an alcoholic. His original choice to abuse alcohol could have disastrous effects on his family that can last for generations, including influencing his children and grandchildren to abuse alcohol. This is not because they are guilty of their father’s sin but because dependency on alcohol is the only way they learned to deal with problems. In that way one can say that the sin of the father has been passed down through generations. It is not the actual fault that is passed down but the consequences of the original sinful choice.