<p>High-resolution bathymetric models are essential for oceanographic research and marine applications. Deep learning methods are increasingly used for bathymetric inversion, typically relying on gridded shipborne soundings as training labels. However, the confidence of these gridded depth values is highly heterogeneous, as they are derived from interpolating sparse and unevenly distributed point measurements. To address this inherent uncertainty in the training data, we propose the Abundance-Constrained Convolutional Neural Network (ABCNN). Our approach introduces an "abundance field" that quantifies ship sounding density, providing a direct measure of confidence for each grid cell. This field is integrated into an adaptive loss function, which weights the learning process to reliable grid cells and reduce the influence of uncertain ones. Experiments show that ABCNN produces more accurate and robust seafloor topography, offering a principled framework that effectively accounts for the varying quality of gridded bathymetric data.</p>