Reassembly tasks play a fundamental role in many fields and multiple approaches exist to solve specific reassembly problems. In this context, we posit that a general unified model can effectively address them all, irrespective of the input data type (image, 3D, etc.). We introduce DiffAssemble, a Graph Neural Network (GNN)-based architecture that learns to solve reassembly tasks using a diffusion model formulation.Our method treats the elements of a set, whether pieces of 2D patch or 3D object fragments, as nodes of a spatial graph. Training is performed by introducing noise into the position and rotation of the elements and iteratively denoising them to reconstruct the coherent initial pose.DiffAssemble achieves state-of-the-art (SOTA) results in most 2D and 3D reassembly tasks and is the first learning-based approach that solves 2D puzzles for both rotation and translation. Furthermore, we highlight its remarkable reduction in run-time, performing 11 times faster than the quickest optimization-based method for puzzle solving.