We propose a mechanism for diffusion generalization based on local denoising operations. Through analysis of network and empirical denoisers, we identify local inductive biases in diffusion models. We demonstrate that local denoising operations can be used to approximate the optimal diffusion denoiser. Using a collection of patch-based, local empirical denoisers, we construct a denoiser which approximates the generalization behaviour of diffusion model denoisers over forward and reverse diffusion processes.