  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 offered by MagicPlan from its
production pipeline, where pieces are room layouts constructed by augmented
reality App by real-estate consumers. The qualitative and quantitative
evaluations demonstrate that our approach outperforms the competing methods by
significant margins in all the tasks.
