Marlins starting pitcher Henderson Alvarez, on the 15-day disabled list with right shoulder inflammation, threw a live batting practice session Tuesday, the Sun Sentinel reported. He is scheduled to throw another one by the end of the week, barring any setbacks.

If his sessions go well, he'll be moved to the minors to start his rehab assignment. General manager Mike Hill told the Sun Sentinel that Alvarez could make his debut at some point in early May.