Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional reasoning. We use the forward process to map elements' positions in a set to random positions in a continuous space. Positional Diffusion learns to reverse the noising process and recover the original positions through an Attention-based Graph Neural Network. We conduct extensive experiments with benchmark datasets including two puzzle datasets, three sentence ordering datasets, and one visual storytelling dataset, demonstrating that our method outperforms long-lasting research on puzzle solving with up to +18% compared to the second-best deep learning method, and performs on par against the state-of-the-art methods on sentence ordering and visual storytelling. Our work highlights the suitability of diffusion models for ordering problems and proposes a novel formulation and method for solving various ordering tasks. Project website at https://iit-pavis.github.io/Positional_Diffusion/
@article{arxiv.2303.11120,
title = {Positional Diffusion: Ordering Unordered Sets with Diffusion Probabilistic Models},
author = {Francesco Giuliari and Gianluca Scarpellini and Stuart James and Yiming Wang and Alessio Del Bue},
journal= {arXiv preprint arXiv:2303.11120},
year = {2023}
}