Solving jigsaw puzzles, a long-standing challenge in both human cognition and artificial intelligence, has seen significant progress with modern computer vision techniques. In this paper, we introduce a diffusion-based framework for jigsaw puzzle reconstruction, leveraging denoising diffusion models to iteratively refine piece placements. Unlike prior methods that rely on anchored reference pieces and relative positioning, our approach directly regresses absolute positions, making it more flexible and generalizable. Additionally, we extend puzzle-solving beyond square pieces by incorporating polygonal partitions and employ DDIM for efficient inference. Our modular pipeline is adaptable to various puzzle formulations, and we demonstrate its effectiveness by achieving state-of-the-art performance on the JPwLEG benchmark.