Positional Diffusion: Ordering Unordered Sets with Diffusion Probabilistic Models

• URL: http://arxiv.org/abs/2303.11120v1
• Date: Mon, 20 Mar 2023 14:01:01 GMT
• Title: Positional Diffusion: Ordering Unordered Sets with Diffusion Probabilistic Models
• Authors: Francesco Giuliari, Gianluca Scarpellini, Stuart James, Yiming Wang, Alessio Del Bue
• Abstract summary: We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models. 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.
• Score: 32.63654140960086
• License: http://creativecommons.org/licenses/by/4.0/
• 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/

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