# Geometry-based Schr"odinger Bridges for Trustworthy Multimodal Fusion

arXiv: https://arxiv.org/abs/2605.31193 · HTML: https://mlsanity.com/paper/2605.31193/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 22 of 22)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [What Makes Training Multi-Modal Classification Networks Hard?](https://mlsanity.com/paper/1905.12681/) (2019)
- [Are Multimodal Transformers Robust to Missing Modality?](https://mlsanity.com/paper/2204.05454/) (2022)
- [Trusted Multi-View Classification with Dynamic Evidential Fusion](https://mlsanity.com/paper/2204.11423/) (2022)
- [MMTM: Multimodal Transfer Module for CNN Fusion](https://mlsanity.com/paper/1911.08670/) (2019)
- [Fast Unsupervised Brain Anomaly Detection and Segmentation with Diffusion Models](https://mlsanity.com/paper/2206.03461/) (2022)
- [Provable Dynamic Fusion for Low-Quality Multimodal Data](https://mlsanity.com/paper/2306.02050/) (2023)
- [Multimodal Representation Learning by Alternating Unimodal Adaptation](https://mlsanity.com/paper/2311.10707/) (2023)
- [Predictive Dynamic Fusion](https://mlsanity.com/paper/2406.04802/) (2024)
- [Multimodal Learning with Uncertainty Quantification based on Discounted Belief Fusion](https://mlsanity.com/paper/2412.18024/) (2024)

## Abstract (arXiv)

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 Schr"odinger 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.