We present a duality relationship between abduction for definite abductive programs and model generation on the only-if part of these programs. As was pointed out by Console et al. (1991), abductive solutions for an abductive program correspond to models of the only-if part. We extend this observation by showing that the procedural semantics of abduction itself can be interpreted dually as a form of model generation on the only-if part. This model generation extends Satchmo with an efficient treatment of equality atoms occurring in the head of rules. It is illustrated how this duality allows to improve current procedures for both abduction and model generation by transferring technical results known for one of these computational paradigms to the other.