Deep visual Simultaneous Localization and Mapping (SLAM) techniques, e.g., DROID, have made significant advancements by leveraging deep visual odometry on dense flow fields. In general, they heavily rely on global visual similarity matching. However, the ambiguous similarity interference in uncertain regions could often lead to excessive noise in correspondences, ultimately misleading SLAM in geometric modeling. To address this issue, we propose a Learnable Gaussian Uncertainty (LGU) matching. It mainly focuses on precise correspondence construction. In our scheme, a learnable 2D Gaussian uncertainty model is designed to associate matching-frame pairs. It could generate input-dependent Gaussian distributions for each correspondence map. Additionally, a multi-scale deformable correlation sampling strategy is devised to adaptively fine-tune the sampling of each direction by a priori look-up ranges, enabling reliable correlation construction. Furthermore, a KAN-bias GRU component is adopted to improve a temporal iterative enhancement for accomplishing sophisticated spatio-temporal modeling with limited parameters. The extensive experiments on real-world and synthetic datasets are conducted to validate the effectiveness and superiority of our method.