Title: Divergence-Free Neural Networks with Application to Image Denoising
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: image denoising, divergence, Stein's unbiased risk estimate, self-supervised learning, incompressible vector fields

Abstract: We introduce a resource-efficient neural network architecture with zero divergence by design, adapted for high-dimensional problems. Our method is directly applicable to image denoising, for which divergence-free estimators are particularly well-suited for self-supervised learning, in accordance with Stein's unbiased risk estimation theory. Comparisons of our parameterization on popular denoising datasets demonstrate that it retains sufficient expressivity to remain competitive with other divergence-based approaches, while outperforming its counterparts when the noise level is known.