Right-hander Matt Magill was released to make room on the 40-man roster for Adcock, who was 0-2 with a 2.96 earned-run average and leading Louisville with 11 saves.
Diaz slipped to 2-1 with a 6.65 ERA over 25 relief appearances after allowing two hits, two walks and the two go-ahead runs to get the decision in Cincinnati's 9-7 loss to San Diego on Saturday.
Magill had successful Tommy John surgery on May 8 to repair the torn ulnar collateral ligament in his right elbow. He is expected to return in 2016. He was acquired in December from the Dodgers in exchange for outfielder Chris Heisey.