GReCF: Generative Recommendation via Continuous-Space Collaborative Filtering

Generative recommendation aims to create and recommend novel items beyond fixed catalogs, addressing users' evolving or unrepresented preferences that existing catalogs cannot adequately capture. It is important to generate content aligned with users' historical preferences while reliably extrapolating beyond observed history. We formulate this task as collaborative preference-field completion in continuous item space, with user-based and item-based collaborative filtering providing two completion mechanisms. We instantiate this formulation in GReCF, our proposed reference-free generative recommender in the image modality. GReCF represents users with adaptive multi-interest themes, anchors each generation to one theme, and injects user and theme conditions into a pretrained diffusion model through residual preference attention. Shared training transfers evidence across users, while masked-interest training learns relations among co-occurring themes to support extrapolation beyond observed history. To support generative recommendation research, we construct CIGR, a synthetic dataset with one million positive interactions. We also introduce an extrapolation-focused evaluation protocol specifically for the generative recommendation task. Across three datasets, GReCF achieves competitive ranking, strong personalization, favorable image quality, high coverage, and reliable CF extrapolation with few unsupported generations. We further investigate the cold-start generation capability of GReCF and show that it preserves initial interests while enabling CF extrapolation.