The AllDifferent constraint is a fundamental tool in Constraint Programming. It naturally arises in many problems, from puzzles to scheduling and routing applications. Such popularity has prompted an extensive literature on filtering and propagation for this constraint. This paper investigates the use of General Processing Units (GPUs) to accelerate filtering and propagation. In particular, the paper presents an efficient parallelization of the AllDifferent constraint on GPU, along with an analysis of different design and implementation choices and evaluation of the performance of the resulting system on several benchmarks.