Unified Framework for Generative Sequential Recommendation

How much variation a generative recommender’s sampler introduces on the way to a sample, its stochasticity level, is a property of the user rather than of the task. A long history already determines the next item, so exploration can only cost; a short history, or interests spanning several catalog categories, leaves the target under-determined. No existing generative recommender can act on this, because none can vary the level at all: it is determined jointly by the interpolant and the training objective. We remove that constraint. Denoising diffusion (DDPM), its deterministic counterpart (DDIM), Flow Matching and Schrödinger Bridges are one SDE at different values of that scalar; the theory unifying them holds it fixed across the population, and extending that theory frees it to be any measurable function of the user, every conditional marginal preserved. The level appears in neither training objective, so a trained checkpoint reproduces these processes at inference rather than committing to one of them before training. Serving it per user pays in diversity at no cost in accuracy, on corpora whose users genuinely differ, and when the next several items are predicted at once.