In one embodiment, the invention is to a process for purifying a by-product stream. The process comprises the step of providing a by-product stream comprising an ammonium salt, dimerized amide, and optionally water. The process further comprises the step of precipitating at least a portion of the dimerized amide in the by-product stream to form solid dimerized amide. The process further comprises the step of separating the solid dimerized amide from the by-product stream to form a treated by-product stream comprising less than 1 wt. % solid dimerized amide.