Fading to Grow: Growing Preference Ratios via Preference Fading Discrete Diffusion for Recommendation

Recommenders aim to rank items from a discrete item corpus in line with user interests, yet suffer from extremely sparse user preference data. Recent advances in diffusion models have inspired diffusion-based recommenders, which alleviate sparsity by injecting noise during a forward process to prevent collapse of perturbed preference distributions. However, current diffusion‑based recommenders predominantly rely on continuous Gaussian noise, which is intrinsically mismatched with the discrete nature of user preference data in recommendation. In this paper, building upon recent advances in discrete diffusion, we propose \textbf{PreferGrow}, a discrete diffusion-based recommender modeling preference ratios by fading and growing user preferences over the discrete item corpus. PreferGrow differs from existing diffusion-based recommenders in three core aspects: (1) Discrete modeling of preference ratios: PreferGrow models relative preference ratios between two items, where a positive value indicates a more preferred one over another less preferred. This formulation aligns naturally with the discrete and ranking-oriented nature of recommendation tasks. (2) Perturbing via preference fading: Instead of injecting continuous noise, PreferGrow fades user preferences by replacing the preferred item with alternatives---physically akin to negative sampling---thereby eliminating the need for any prior noise assumption. (3) Preference reconstruction via growing: PreferGrow reconstructs user preferences by iteratively growing the preference signal from the estimated ratios. We further provide theoretical analysis showing that PreferGrow preserves key properties of discrete diffusion processes. PreferGrow provides a well-defined matrix‑based formulation for discrete diffusion-based recommendation and empirically outperforms existing diffusion‑based recommenders across five benchmark datasets, underscoring its superior effectiveness. Our codes are available at \url{https://anonymous.4open.science/r/PreferGrow_Commit-2259/}.