This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks.In the latter task, for instance, the proposed system ``PuzzleFusion'' takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations, akin to solving the jigsaw puzzle of room layouts. A surprising discovery of the paper is that the simple use of a Diffusion Model effectively solves these challenging spatial puzzle tasks as a conditional generation process. To enable learning of an end-to-end neural system, the paper introduces new datasets with ground-truth arrangements: 1) 2D Voronoi Jigsaw Dataset, a synthetic one where pieces are generated by voronoi diagram of 2D pointset; and 2) MagicPlan Dataset, a real one from a production pipeline by MagicPlan, where pieces are room layouts constructed by augmented reality App by real-estate consumers.The qualitative and quantitative evaluations demonstrate that the proposed approach outperforms the competing methods by significant margins in all three spatial puzzle tasks. We have provided code and data in https://sepidsh.github.io/puzzlefusion.