Nelson (elbow) threw live batting practice Tuesday, Alex Weiner of ArizonaSports.com reports.
Tuesday marks the first time Nelson has faced hitters since he landed on the injured list back in June with a strained right elbow. He threw 21 pitches during his first live session but is expected to be brought back as a reliever, so he won't need to spend time building up his workload. The 28-year-old righty said he is hopeful to begin pitching in rehab games soon, though the Diamondbacks haven't indicated when he might begin a minor-league assignment.