Compact Representations of Divergence-Free Fields for Self-Supervised Image Denoising

We show that divergence-free vector fields admit parsimonious representations, thus extending the classical curl representation beyond three dimensions. Building on this foundation, we propose a novel computationally efficient network architecture that enforces zero divergence by design. Experiments on image denoising—a setting where divergence-free fields are amenable to learning without ground-truth data—demonstrate that our approach sets a new benchmark for constraint-based methods under Gaussian noise, as well as Poisson and real-world noise with minor architectural modifications, bridging the performance gap with leading denoisers.