Diffusion models (DMs) have recently gained significant interest for their exceptional potential in recommendation tasks. This stems primarily from their prominent capability in distilling, modeling, and generating comprehensive user preferences. However, previous work fails to examine DMs in recommendation tasks through a rigorous lens. In this paper, we first experimentally investigate the completeness of recommender models from a thermodynamic view. We reveal that existing DM-based recommender models operate by maximizing the energy, while classic recommender models operate by reducing the entropy. Based on this finding, we propose a minimalistic diffusion framework that incorporates both factors via the maximization of Helmholtz free energy. Meanwhile, to foster the optimization, our reverse process is armed with a well-designed denoiser to maintain the inherent anisotropy, which measures the user-item cross-correlation in the context of bipartite graphs. Finally, we adopt an Acceptance-Rejection Gumbel Sampling Process (AR-GSP) to prioritize the far-outnumbered unobserved interactions for model robustness. AR-GSP integrates an acceptance-rejection sampling to ensure high-quality hard negative samples for general recommendation tasks, and a timestep-dependent Gumbel Softmax to handle an adaptive sampling strategy for diffusion models. Theoretical analyses and extensive experiments demonstrate that our proposed framework has distinct superiority over baselines in terms of accuracy and efficiency.

Despite their success in Collaborative Filtering (CF), Graph Convolutional Networks (GCNs) are often viewed as Low-pass Graph Filters (LGFs) with task-specific supervision, while the influence of the underlying graph's spectral properties on LGF performance remains underexplored. Our analysis reveals that the performance of LGFs is strongly affected by algebraic connectivity. When connectivity is strong, LGFs tend to perform well; when it is weak, their effectiveness diminishes noticeably. This spectral sensitivity highlights an important limitation of existing models. To address this limitation, we propose Graph Booster, a learnable module that adaptively improves graph connectivity by reweighting edges. Unlike heuristic preprocessing, Graph Booster identifies bottleneck edges via spectral embeddings and adjusts their weights with a monotonic network guided by a lightweight graph connectivity regularizer. Integrated into LightGCN framework, our model BoostGCN achieves improvements over state-of-the-art methods, underscoring the significance of algebraic connectivity for graph-based CF.

The structural heterogeneity of user-item interaction graphs poses a fundamental challenge for graph-based recommender systems. While Graph Convolutional Networks (GCNs) have achieved remarkable success in collaborative filtering, their uniform low-pass filtering nature often fails to accommodate the varying spectral needs of nodes with different local structures, resulting in suboptimal performance. To address this issue, we propose a Structurally Sensitive Adaptive Graph Filter, dubbed as SSAGF, a novel framework that enables structure-aware filtering on user-item graphs. SSAGF first clusters nodes based on local structural properties, then learns customized filters per group by reinterpreting the convolutional depth in GCNs. This adaptive mechanism ensures that nodes with distinct structural roles are treated appropriately, enhancing both accuracy and fairness without significantly increasing model complexity. To further improve scalability, SSAGF avoids costly eigenvalue decompositions by approximating spectral filters through Maclaurin series expansion, transforming the convolution into a pooling-like operation over standard GCN outputs. Extensive experiments on four benchmark datasets demonstrate that SSAGF consistently outperforms competitive baselines, especially in scenarios with high structural heterogeneity, offering a principled and efficient solution for structure-aware recommendation.

In graph-based multimedia recommendation, accurately modeling item-item semantic similarity is crucial for constructing high-quality semantic structures. However, multimodal content often exhibits semantic inconsistencies across modalities, resulting in noisy or misleading similarity signals. We refer to this as modality mismatching, where unaligned representations, such as an image conveying semantics unrelated to its accompanying text, undermine the reliability of feature-based similarity estimation. Importantly, modality consistency is context sensitive, varying with the underlying semantic environment in which modalities are interpreted. This highlights the necessity of jointly modeling modality reliability and contextual semantics. To address this challenge, we propose RGSLMRec, a robust graph structure learning framework that models and exploits the semantic reliability of multimodal features under diverse contexts. At its core, RGSLMRec builds on the invariant learning paradigm and introduces two key innovations: (i) it simulates multiple perturbed semantic environments and employs environment-specific monotonic networks to estimate reliability; and (ii) it adopts a risk-invariant objective based on Variance Risk Extrapolation to enforce the learning of invariant reliability across environments. On top of this, (iii) RGSLMRec constructs reliability-guided item-item graphs and captures collaborative and semantic signals via a hybrid early-late fusion strategy. Extensive experiments on several real-world datasets and additional synthetically perturbed datasets demonstrate that RGSLMRec not only outperforms strong baselines but also exhibits superior robustness to modality mismatching.

Social recommendation systems leverage the social relations among users to deal with the inherent cold-start problem in user-item interactions. However, previous models only treat the social graph as the static auxiliary to the user-item interaction graph, rather than dig out the hidden essentials and optimize them for better recommendations. Thus, the potential of social influence is still under-explored. In this paper, we will fill this gap by proposing a novel model for social influence learning to derive the essential influence patterns within the user relationships. Our model views the social influence from the perspectives of (1) the diversity of neighborhood's influence on the users, (2) the disentanglement of neighborhood's influence on the users, and (3) the exploration of underlying implicit social influence. To this end, we first employ a novel layerwise graph-enhanced variational autoencoder for the reconstruction of neighborhoods' representations, which aims to learn the pattern of social influence as well as simulate the social profile of each user for overcoming the sparsity issue in social relation data. Meanwhile, we introduce a layerwise graph attentive network for capturing the most influential scope of neighborhood. Finally, we adopt a dual sampling process to generate new social relations for enhancing the social recommendation. Extensive experiments have been conducted on three widely-used benchmark datasets, verifying the superiority of our proposed model compared with the representative approaches.