Continuous-time Discrete-space Diffusion Model for Recommendation

TL;DR

CDRec introduces a continuous-time, discrete-space diffusion framework for recommendations that operates over historical interactions via an absorbing-state masking mechanism. A popularity-aware forward diffusion schedule preserves signals from popular items, while a consistency-based reverse process parameterization enables efficient single-step or iterative generation. The framework is augmented with contrastive guidance to incorporate multi-hop collaborative signals, yielding superior accuracy and efficiency across real-world datasets. This approach advances diffusion-based recommender systems by explicitly modeling discrete interaction distributions in continuous time and leveraging domain knowledge to improve sampling and personalization.

Abstract

In the era of information explosion, Recommender Systems (RS) are essential for alleviating information overload and providing personalized user experiences. Recent advances in diffusion-based generative recommenders have shown promise in capturing the dynamic nature of user preferences. These approaches explore a broader range of user interests by progressively perturbing the distribution of user-item interactions and recovering potential preferences from noise, enabling nuanced behavioral understanding. However, existing diffusion-based approaches predominantly operate in continuous space through encoded graph-based historical interactions, which may compromise potential information loss and suffer from computational inefficiency. As such, we propose CDRec, a novel Continuous-time Discrete-space Diffusion Recommendation framework, which models user behavior patterns through discrete diffusion on historical interactions over continuous time. The discrete diffusion algorithm operates via discrete element operations (e.g., masking) while incorporating domain knowledge through transition matrices, producing more meaningful diffusion trajectories. Furthermore, the continuous-time formulation enables flexible adaptive sampling. To better adapt discrete diffusion models to recommendations, CDRec introduces: (1) a novel popularity-aware noise schedule that generates semantically meaningful diffusion trajectories, and (2) an efficient training framework combining consistency parameterization for fast sampling and a contrastive learning objective guided by multi-hop collaborative signals for personalized recommendation. Extensive experiments on real-world datasets demonstrate CDRec's superior performance in both recommendation accuracy and computational efficiency.

Figures (9)

• Figure 1: Comparison of diffusion-based recommender systems across different state-spaces. Continuous-space diffusion algorithms apply isotropic Gaussian noise to either the collaborative graph’s adjacency matrix or the encoded representations, often compromising personalized information in the embedding space. In contrast, discrete-space diffusion models directly operate through item-level operations toward a uniform distribution. Inspired by this formulation, our proposed CDRec method perturbs historical interactions via masking operations in continuous time, enabling state transitions to occur at arbitrary time steps.
• Figure 2: The proposed CDRec framework comprises three main modules: popularity-aware noise schedule, consistency-driven diffusion parameterization, and contrastive-guided diffusion. The left panel illustrates the forward diffusion process, where state transitions are controlled by item popularity to simulate interaction dynamics. The right panel presents the reverse generation modeling process, which leverages a consistency function for efficient parameterization and applies contrastive learning to guide personalized recommendations with the structural collaborative signal.
• Figure 3: Absorbing probability for items with varying popularity deviation ($\omega=0.5$).
• Figure 4: Ablation study of CDRec and its variants on three datasets with evaluation metrics Recall@10 and NDCG@10.
• Figure 5: Effect of sampling steps $N$ on Recall@10 and NDCG@10.