In real-world recommender systems, implicitly collected user feedback, while abundant, often includes noisy false-positive and false-negative interactions. The possible misinterpretations of the user-item interactions pose a significant challenge for traditional graph neural recommenders. These approaches aggregate the users' or items' neighbours based on implicit user-item interactions in order to accurately capture the users' profiles. To account for and model possible noise in the users' interactions in graph neural recommenders, we propose a novel Diffusion Graph Transformer (DiffGT) model for top-k recommendation. Our DiffGT model employs a diffusion process, which includes a forward phase for gradually introducing noise to implicit interactions, followed by a reverse process to iteratively refine the representations of the users' hidden preferences (i.e., a denoising process). In our proposed approach, given the inherent anisotropic structure observed in the user-item interaction graph, we specifically use anisotropic and directional Gaussian noises in the forward diffusion process. Our approach differs from the sole use of isotropic Gaussian noises in existing diffusion models. In the reverse diffusion process, to reverse the effect of noise added earlier and recover the true users' preferences, we integrate a graph transformer architecture with a linear attention module to denoise the noisy user/item embeddings in an effective and efficient manner. In addition, such a reverse diffusion process is further guided by personalised information (e.g., interacted items) to enable the accurate estimation of the users' preferences on items. Our extensive experiments conclusively demonstrate the superiority of our proposed graph diffusion model over ten existing state-of-the-art approaches across three benchmark datasets.

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