{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/positional-diffusion-ordering-unordered-sets","title":"Positional Diffusion: Ordering Unordered Sets with Diffusion Probabilistic Models","arxiv_id":"2303.11120","date":"2023-03-20","proceeding":null,"authors":["Francesco Giuliari","Gianluca Scarpellini","Stuart James","Yiming Wang","Alessio Del Bue"],"abstract":"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/","url_abs":"https://arxiv.org/abs/2303.11120v1","url_pdf":"https://arxiv.org/pdf/2303.11120v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"positional-diffusion-ordering-unordered-sets","repo_url":"https://github.com/IIT-PAVIS/Positional_Diffusion","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"},{"task_slug":"sentence","task_name":"Sentence"},{"task_slug":"sentence-ordering","task_name":"Sentence Ordering"},{"task_slug":"visual-storytelling","task_name":"Visual Storytelling"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2303.11120","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}