Positional diffusion: Graph-based diffusion models for set ordering

Giuliari, Francesco; Scarpellini, Gianluca; Fiorini, Stefano; James, Stuart; Morerio, Pietro; Wang, Yiming; Del Bue, Alessio

Abstract

Positional reasoning is the process of ordering an unsorted set of parts into a consistent structure. To address this problem, we present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models. Using a diffusion process, we add Gaussian noise to the set elements’ position and map them to a random position in a continuous space. Positional Diffusion learns to reverse the noising process and recover the original positions through an Attention-based Graph Neural Network. To evaluate our method, we conduct extensive experiments on three different tasks and seven datasets, comparing our approach against the state-of-the-art methods for visual puzzle-solving, sentence ordering, and room arrangement, demonstrating that our method outperforms long-lasting research on puzzle solving with up to +17% compared to the second-best deep learning method, and performs on par against the state-of-the-art methods on sentence ordering and room rearrangement. Our work highlights the suitability of diffusion models for ordering problems and proposes a novel formulation and method for solving various ordering tasks.

Citation

Giuliari, F., Scarpellini, G., Fiorini, S., James, S., Morerio, P., Wang, Y., & Del Bue, A. (2024). Positional diffusion: Graph-based diffusion models for set ordering. Pattern Recognition Letters, 186, 272-278. https://doi.org/10.1016/j.patrec.2024.10.010

• Journal Article Type: Article
• Acceptance Date: Oct 17, 2024
• Online Publication Date: Oct 23, 2024
• Publication Date: 2024-10
• Deposit Date: Nov 26, 2024
• Publicly Available Date: Nov 26, 2024
• Journal: Pattern Recognition Letters
• Print ISSN: 0167-8655
• Electronic ISSN: 1872-7344
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 186
• Pages: 272-278
• DOI: https://doi.org/10.1016/j.patrec.2024.10.010
• Public URL: https://durham-repository.worktribe.com/output/3107073