Provably Robust Multimodal Fusion under Conditional Dependence Shift

Multimodal robustness is usually studied by corrupting or degrading individual modalities. We study a different failure mode where the quality distribution of each modality remains unchanged while the dependence among their local quality states changes. We call this conditional dependence shift (CDS). Under CDS, every modality experiences the same corruption marginal, yet fusion can still fail because local failures co occur differently across modalities, changing the temporal overlap of jointly reliable evidence. We characterize exactly when fusion risk is invariant to such quality couplings, derive an exact decomposition of the resulting risk shift, and introduce a coupling-sensitivity modulus that tightly bounds risk variation under every coupling with the same modality marginals and is computable by a small linear program. These results yield StableFuse, which aggregates evidence and reliability within each modality and directly regularizes a differentiable upper bound on this modulus, so that robustness to coupling shifts is explicitly controlled rather than only encouraged. Using controlled within sample protocols that preserve individual modality quality while changing only the coupling of local failures, StableFuse improves average and worst case CDS performance across four multimodal benchmarks while reducing the certified modulus and preserving clean accuracy.