Drifting with Intent: Generative Interest Trajectories for Multimodal Web Recommendation

User interest is not static but rather a continuously evolving process shaped by diverse interactions across multimodal web platforms. Traditional recommendation systems often model user preferences as discrete snapshots or oversimplified trajectories, failing to capture the nuanced dynamics of interest evolution. In this work, we propose Drifting with Intent, a novel framework that formalizes user interest as a continuous-time stochastic process governed by spatio-temporal coupled stochastic differential equations (SDEs). Our approach fundamentally departs from diffusion-based methods by modeling interest evolution as a directed drift toward meaningful content rather than random diffusion. The core innovation lies in a multi-granularity hypergraph encoder that captures cross-scale user-item interactions, coupled with a unified SDE solver that generates personalized interest trajectories across temporal and relational dimensions. Unlike prior work employing redundant twin networks, we introduce a generative-discriminative co-optimization framework that efficiently balances content generation and recommendation precision within a single parameter space. Extensive experiments across eight diverse datasets demonstrate that our framework not only outperforms state-of-the-art methods in recommendation quality but also provides interpretable interest trajectories that reveal how user preferences evolve across different modalities and time scales. Our work bridges the gap between generative modeling and practical recommendation systems by treating user interest as a purposeful drift rather than a random walk.