## 1 Introduction  
Bathymetric super-resolution reconstruction (BSRR), situated at the intersection of marine geophysics and artificial intelligence, addresses the fundamental challenge of reconstructing high-resolution seafloor topography with rich details from sparse shipborne sonar data or low-resolution satellite altimetry. This technology not only supports marine resource exploration, geological structure analysis, and navigational safety [1, 2, 3] but also constitutes a critical component of modern marine research. Traditional seafloor mapping techniques primarily rely on multibeam and side-scan sonar; however, these methods are limited by sensor resolution [4], environmental noise [5], and data sparsity [6], making the accurate recovery of high-frequency details in complex terrains such as seamounts and fault zones particularly challenging. To mitigate data insufficiency, traditional interpolation methods--including linear, polynomial, inverse distance weighting, Kriging, and spline interpolation--have been employed [7; 8; 9; 10; 11]. Nevertheless, these methods often struggle with noise suppression and the recovery of fine details [12; 13]. In recent years, deep learning techniques have made significant strides in image super-resolution. Approaches such as SRCNN [14], proposed by [PERSON] et al., and VDSR [15], designed by [PERSON] et al., have markedly improved reconstruction accuracy through deep convolutional networks, while generative adversarial networks (GANs), such as SRGAN [16], further enhance image realism. Notably, multi-scale convolutional networks [15] applied to seafloor image super-resolution have considerably improved the recovery of high-frequency details [17; 18], thereby offering innovative tools for seafloor topography reconstruction. However, existing deep learning methods typically yield deterministic reconstruction results and fail to address the ill-posed nature of mapping a single low-resolution input to multiple plausible high-resolution outputs [19; 20]. This shortfall can introduce bias and unreliability in downstream processing, especially in morphologically complex seafloor environments. Uncertainty quantification--which involves both data-related aleatoric uncertainty and model-related epistemic uncertainty [21]--is essential for overcoming these challenges. Bayesian deep learning provides a rigorous framework for modeling uncertainty, with [PERSON] and [PERSON] demonstrating that MC-Dropout during inference can serve as a Bayesian approximation method through repeated sampling [22]. [PERSON] and [PERSON] further investigated the joint modeling of both types of uncertainty [19], proposing an improved Bayesian inference strategy for remote sensing data that lays a theoretical foundation for uncertainty estimation in complex environments. Nonetheless, standard MC-Dropout employs a fixed dropout rate, which may be inadequate for capturing local feature variations in complex seafloor topography, potentially leading to insufficient local detail capture [23]. Consequently, adaptive dropout methods have been introduced in recent years to dynamically adjust dropout rates based on input features, thereby enhancing detail recovery [24; 25; 26; 27]. Moreover, GAN-based reconstruction methods have provided novel perspectives on uncertainty quantification by synergistically improving detail preservation and visual fidelity [28]. Although deep ensemble methods excel in uncertainty estimation, their high computational cost limits practical application [29]. Therefore, developing an efficient and precise method for jointly modeling complex seafloor features and reliably quantifying uncertainty remains an urgent scientific challenge. This study introduces a hybrid Bayesian deep learning framework that integrates MC-Dropout with adaptive dropout. Through multiple forward passes, this framework constructs a predictive distribution while dynamically adjusting local feature extraction [30; 31; 32].