Title: Collaborative Filtering Based on Diffusion Models: Unveiling the Potential of High-Order Connectivity

Abstract: A recent study has shown that diffusion models are well-suited for modeling the generative process of user-item interactions in recommender systems due to their denoising nature. However, existing diffusion model-based recommender systems do not explicitly leverage high-order connectivities that contain crucial collaborative signals for accurate recommendations. Addressing this gap, we propose CF-Diff, a new diffusion model-based collaborative filtering (CF) method, which is capable of making full use of collaborative signals along with multi-hop neighbors. Specifically, the forward-diffusion process adds random noise to user-item interactions, while the reverse-denoising process accommodates our own learning model, named cross-attention-guided multi-hop autoencoder (CAM-AE), to gradually recover the original user-item interactions. CAM-AE consists of two core modules: 1) the attention-aided AE module, responsible for precisely learning latent representations of user-item interactions while preserving the model's complexity at manageable levels, and 2) the multi-hop cross-attention module, which judiciously harnesses high-order connectivity information to capture enhanced collaborative signals. Through comprehensive experiments on three real-world datasets, we demonstrate that CF-Diff is (a) Superior: outperforming benchmark recommendation methods, achieving remarkable gains up to 7.29% compared to the best competitor, (b) Theoretically-validated: reducing computations while ensuring that the embeddings generated by our model closely approximate those from the original cross-attention, and (c) Scalable: proving the computational efficiency that scales linearly with the number of users or items.