Tightening Multimodal Regression Generalization Bounds via Structured Predictive Distributions

Multimodal regression is increasingly being deployed in real-world applications, yet its generalization performance remains limited, particularly under noisy conditions. Existing methods predominantly rely on point-wise predictions, leaving the role of structured predictive representations in generalization-bound tightening underexplored. In this work, we propose Structured Predictive Distributions (SPD) for tightening generalization bounds in multimodal regression, a theoretically grounded framework that reformulates multimodal regression in a structured predictive distribution space. Concretely, SPD combines Normal-Inverse-Gamma predictive representations with regularization to structure continuous regression outputs and performs multimodal fusion within this structured space. We further introduce a distribution-aware reweighting mechanism that adapts optimization to the predictive representation to improve robustness under noisy conditions. Using a common squared error risk, our analysis establishes tighter generalization bounds through NIG-induced capacity control. We further characterize the empirical-risk condition for comparisons with a matched reference predictor, relating empirical fit to the reduction in the complexity term. Extensive experiments on multiple multimodal regression benchmarks, covering image fusion, crowd counting, and depth estimation, demonstrate that SPD consistently improves robustness under diverse noise conditions. Our code is available in the supplementary material and https://anonymous.4open.science/r/SPD-A356/.