A processing machine (10) for building an object (11) from powder (12) includes a build platform (26A); a powder supply assembly (18) that deposits the powder (12) onto the build platform (26A) to form a powder layer (13); and an energy system (22) that directs an energy beam (22D) at a portion of the powder (12) on the build platform (26A) to form a portion of the object (11). The powder supply assembly (18) can include (i) a powder container (640A) that retains the powder (12); (ii) a supply outlet (639) positioned over the build platform (26A); and (ii) a flow control assembly (642) that selectively controls the flow of the powder (12) from the supply outlet (639).