Astronomical source deblending is the process of separating the contribution of individual stars or galaxies (sources) to an image comprised of multiple, possibly overlapping sources. Astronomical sources display a wide range of sizes and brightnesses and may show substantial overlap in images. Astronomical imaging data can further challenge off-the-shelf computer vision algorithms owing to its high dynamic range, low signal-to-noise ratio, and unconventional image format. These challenges make source deblending an open area of astronomical research, and in this work, we introduce a new approach called Partial-Attribution Instance Segmentation that enables source detection and deblending in a manner tractable for deep learning models. We provide a novel neural network implementation as a demonstration of the method.