Geometry-based Schrödinger Bridges for Trustworthy Multimodal Fusion

Real-world multimodal systems must be robust against low-quality data, such as sensor noise, incomplete multimodal data and conflicting inputs. However, existing trustworthy fusion methods rely on the model's own prediction confidence to judge data quality. This creates a circular dependency: when a model is confident but wrong, these methods fail to detect the error. To break this loop, we propose Geometry-based Multimodal Fusion (GMF). Instead of relying on predictions, we evaluate reliability by measuring how much transport correction the input needs in latent space. We implement Diffusion Schrödinger Bridge transport with Rectified Flow, where the squared initial velocity gives an efficient learned correction score. Valid data has low squared velocity magnitude, while noisy, incomplete data or conflicting data requires stronger transport correction. This geometry-based reliability signal acts as an independent judge, effectively flagging unreliable inputs even when the classifier is fooled. Extensive experiments demonstrate that GMF significantly improves robustness against severe sensor noise and semantic conflicts compared to confidence-based baselines.

Inconsistency-aware Multimodal Schrödinger Bridge for Deepfake Localization

Audio-visual deepfake localization demands interval-level outputs that serve as temporal evidence. Despite recent progress, symmetric fusion under single-sided or asynchronous forgeries propagates cross-modal noise, degrading high-precision localization. We present IaMSB, an inconsistency-aware multimodal Schrödinger Bridge (SB) that jointly estimates cross-modal consistency and performs interval-level localization. Unlike diffusion models, SB minimizes path-distribution discrepancy and yields consistency scores without explicit noise injection or denoising. With the Schrödinger Bridge (SB), IaMSB unifies consistency estimation, cross-modal information selection, and bridge-step scheduling in one framework. Specifically, a lightweight coarse bridge first proposes candidate intervals and estimates cross-modal consistency; these statistics select cross-modal witness signals and allocate bridge steps asymmetrically across modalities. A refinement bridge then performs step-tuned fusion and outputs refined, time-aligned intervals. IaMSB anticipates single-sided and asynchronous forgeries and, using bottlenecked cross-modal interaction with step allocation, suppresses noise transfer, avoids unnecessary iterations. Across benchmarks, IaMSB stabilizes strict-IoU boundary precision, raising AP@0.95 by 3%~10%, and yields improved high-precision localization, particularly for single-sided forgeries.

Generalized Multimodal Fusion via Poisson-Nernst-Planck Equation

Previous studies have highlighted significant advancements in multimodal fusion. Nevertheless, such methods often encounter challenges regarding the efficacy of feature extraction, data integrity, consistency of feature dimensions, and adaptability across various downstream tasks. This paper proposes a generalized multimodal fusion method (GMF) via the Poisson-Nernst-Planck (PNP) equation, which adeptly addresses the aforementioned issues. Theoretically, the optimization objective for traditional multimodal tasks is formulated and redefined by integrating information entropy and the flow of gradient backward step. Leveraging these theoretical insights, the PNP equation is applied to feature fusion, rethinking multimodal features through the framework of charged particles in physics and controlling their movement through dissociation, concentration, and reconstruction. Building on these theoretical foundations, GMF disassociated features which extracted by the unimodal feature extractor into modality-specific and modality-invariant subspaces, thereby reducing mutual information and subsequently lowering the entropy of downstream tasks. The identifiability of the feature's origin enables our approach to function independently as a frontend, seamlessly integrated with a simple concatenation backend, or serve as a prerequisite for other modules. Experimental results on multiple downstream tasks show that the proposed GMF achieves performance close to the state-of-the-art (SOTA) accuracy while utilizing fewer parameters and computational resources. Furthermore, by integrating GMF with advanced fusion methods, we surpass the SOTA results.