Not All Slots Are Equal: Non-Co-Progressive Markov Bridge for Bundle Construction

Bundle construction (BC) is a critical technique in recommender systems research, which aims to select a coherent subset of items from large-scale item catalogs to either construct a complete bundle from scratch or complete a partial bundle with missing items. However, the extremely high-dimensional combinatorial spaces and heterogeneous semantic granularities involved pose significant challenges to BC benchmarking, and existing generative frameworks suffer from failing to precisely align the generated unknown slots with highly compatible known items. In this paper, we exploit conditional probability transitions in discrete state spaces and introduce a novel Non-co-progressive Markov bridge, NonMBB, a generalization of Markov bridge for constructing bundles of products. Specifically, given bundle's unique properties, NonMBB first improve Markov bridge for slot modeling through: i) categorizing item slots into high-compatibility slots and weakly-associated slots with respect to the known items, assigning them distinct timestep schedules to avoid the pitfall where high-compatibility slots must reference noisy, uninformative context at identical noise levels; ii) applying introduce schedule reweighting to constrain the maximum timestep disparity across slots, thereby preventing noise residuals caused by excessive asynchrony. Extensive experiments on Spotify and POG demonstrate that NonMBB establishes a substantially improved optimal bipartite matching over existing diffusion methods, yielding higher embedding-space alignment independently of exact-match recall.