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/

翻译：位置推理是将集合中的无序元素排序为一致结构的过程。我们提出了一种即插即用的图形式化方法——位置扩散（Positional Diffusion），结合扩散概率模型来解决位置推理问题。我们利用前向过程将集合中元素的位置映射到连续空间中的随机位置。位置扩散学习通过基于注意力机制的图神经网络逆转噪声过程并恢复原始位置。我们在包含两个拼图数据集、三个句子排序数据集和一个视觉故事讲述数据集的基准数据集上进行了大量实验，结果表明，与第二优的深度学习方法相比，我们的方法在拼图求解上的性能提升高达18%，并且在句子排序和视觉故事讲述任务上与现有最先进方法表现相当。我们的工作凸显了扩散模型在排序问题中的适用性，并提出了一种解决多种排序任务的新颖形式化方法与方案。项目网站：https://iit-pavis.github.io/Positional_Diffusion/