When a noun loses its substantive sense (as an object) and is rather used as a qualifier, articles can sometimes be omitted.

For example, "je suis étudiant" instead of "je suis un étudiant". The noun here is acting in a more adjective sense.

The same applies to "souvenirs de famille". It means more memories related to the family, rather than the memories belonging to the family exclusively.

You can also say "les membres de famille" for family members, usually used in relation of someone, e.g. "les membres de famille de travailleurs hautement qualifiés". The "famille" here is non-specific but rather attributive (like an adjective).

In English, similar qualifier nouns can usually be added as an adjective before a noun. Consider the nuances between "family members" and "members of the family", "family secret" and "secret of the family" and similar constructions.