Image smoothing with edge preservation in the presence of outliers is a challenge in image processing. Anisotropic diffusion smoothing is a well-established paradigm in digital image smoothing with edge preservation. Anisotropic diffusion smoothing filters are not robust to impulse noise. They employ two or more stages for robustness in the presence of outliers, and, therefore, they demand significantly increased arithmetic operations for robustness; consequently, they are not power efficient. This paper introduces a low arithmetic complexity image smoothing model and proposes an intrinsically robust and power efficient algorithm for anisotropic diffusion smoothing of images. The algorithm outperforms the foundational robust smoothing algorithms in terms of the standard performance metrics and visual quality. © 2019, The Author(s).