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 the 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 PreferGrow, a discrete diffusion-based recommender system that models 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 item pairs, rather than operating in the item representation or raw score simplex. 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 signals from the estimated ratios. PreferGrow offers a well-defined matrix-based formulation with theoretical guarantees on Markovianity and reversibility, and it demonstrates consistent performance gains over state-of-the-art diffusion-based recommenders across five benchmark datasets, highlighting both its theoretical soundness and empirical effectiveness.