Evidence-Lattice Flow: Task-Posterior Transport and Integration for Incomplete Multimodal Learning

Incomplete multimodal learning (IML) aims to make reliable predictions when some input modalities are unavailable. Many existing methods reconstruct missing inputs or map incomplete observations to a single complete-like representation. This completion-centric strategy collapses ambiguous evidence into a single representation, which may obscure variation among plausible task outcomes and lead to overconfident predictions. To address this issue, we propose Evidence-Lattice Flow (ELF), a general framework that recasts IML as task-posterior inference over an evidence lattice. Each lattice node represents an available modality subset and carries the posterior supported by that evidence. ELF implements this view through three stages. Full-Evidence Task Anchoring establishes task semantics from complete observations, Lattice-Conditioned Flow Transport moves stochastic particles toward subset-specific task-latent distributions, and Posterior Task Integration converts transported samples into predictions and uncertainty. ELF thus learns evidence-conditioned task-latent distributions and integrates predictions from transported samples, without reconstructing missing modalities. We characterize consistency relations among underlying task posteriors and relate transport error to downstream risk. Experiments on five datasets spanning emotion recognition, sentiment analysis, and action quality assessment demonstrate ELF's effectiveness. Relative to the strongest baseline, ELF reduces MSE averaged over six incomplete modality subsets by 8.7% on FS1000 and 4.9% on Fis-V.