Image coaddition is of critical importance to observational astronomy. This family of methods consisting of several processing steps such as image registration, resampling, deconvolution, and artifact removal is used to combine images into a single higher-quality image. An alternative to these methods that are built upon vectorized operations is the representation of an image function as a neural network, which has had considerable success in machine learning image processing applications. We propose a deep learning method employing gradient-based planar alignment with Bundle-Adjusting Radiance Fields (BARF) to combine, de-noise, and remove obstructions from observations of cosmological objects at different resolutions, seeing, and noise levels -- tasks not currently possible within a single process in astronomy. We test our algorithm on artificial images of star clusters, demonstrating powerful artifact removal and de-noising.