  This paper presents PolyDiffuse, a novel structured reconstruction algorithm
that transforms visual sensor data into polygonal shapes with Diffusion Models
(DM), an emerging machinery amid exploding generative AI, while formulating
reconstruction as a generation process conditioned on sensor data. The task of
structured reconstruction poses two fundamental challenges to DM: 1) A
structured geometry is a ``set'' (e.g., a set of polygons for a floorplan
geometry), where a sample of $N$ elements has $N!$ different but equivalent
representations, making the denoising highly ambiguous; and 2) A
``reconstruction'' task has a single solution, where an initial noise needs to
be chosen carefully, while any initial noise works for a generation task. Our
technical contribution is the introduction of a Guided Set Diffusion Model
where 1) the forward diffusion process learns guidance networks to control
noise injection so that one representation of a sample remains distinct from
its other permutation variants, thus resolving denoising ambiguity; and 2) the
reverse denoising process reconstructs polygonal shapes, initialized and
directed by the guidance networks, as a conditional generation process subject
to the sensor data. We have evaluated our approach for reconstructing two types
of polygonal shapes: floorplan as a set of polygons and HD map for autonomous
cars as a set of polylines. Through extensive experiments on standard
benchmarks, we demonstrate that PolyDiffuse significantly advances the current
state of the art and enables broader practical applications.
