Deformable Polygonal Flow Matching with Informed Priors and Hierarchical Graph Constraints
Arnaud Gueze, Matthieu Ospici, Damien Rohmer, Marie-Paule Cani
Abstract
This paper presents a novel method, called Deformable Polygonal Flow Matching (DPFM), for the generation of polygonal arrangements such as jigsaw puzzles and floor plans. DPFM is a Flow Matching framework that enables the generation process to deform, rotate, and translate polygons while decoupling these transformations, allowing to toggle them individually. Able to combine the spatial reasoning capabilities of arrangement models with the flexibility of position-based models, it covers a wide range of applications within a unified formulation, from noiseless puzzle solving using rigid alignments to unconstrained floor plan generation.We represent data using a hierarchical graph composed of a topological subgraph encoding connectivity information and semantics (such as room types for floor plans), and a geometrical subgraph encoding the 1D polygonal loop of each shape. DPFM also leverages Flow Matching
BibTeX
@inproceedings{aaai2026_deformablepolygo,
title = {Deformable Polygonal Flow Matching with Informed Priors and Hierarchical Graph Constraints},
author = {Arnaud Gueze and Matthieu Ospici and Damien Rohmer and Marie-Paule Cani},
booktitle = {AAAI 2026},
year = {2026}
}