Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising

Normalization Equivariance (NE), equivariance to global contrast and brightness transforms, improves robustness to distribution shift in image-to-image prediction. Existing methods enforce this prior by constraining internal layers to NE-compatible families, limiting compatibility with standard components (e.g., attention, LayerNorm) and adding runtime cost. We prove that a function is NE if and only if it admits a normalize-process-denormalize factorization. Using this characterization, we construct a parameter-free wrapper (WNE) that enforces input-output NE around any backbone, including transformers. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable overhead on GPU, while architectural NE baselines incur up to a $1.6\times$ slowdown.