An image diffusion method based on the adaptive smoothing approach proposed by Saint-Marc et al. (1991) is presented. We first investigate the behavior of the adaptive smoothing approach for computing simplifications of an input image, a basic problem in image analysis. Whereas the original adaptive smoothing algorithm achieves satisfactory results for 1-D signals, the unequal strength of the boundaries of images (2-D signals) poses a difficult problem. We propose the addition of an edge-strengthening step that addresses that problem. Results show significant improvements. However, this added step requires us to (1) extract a set of edge pixels and (2) obtain certain edge information (in particular, edge-side location). These tasks are interrelated, and their computation is described. In addition, the limitations of the adaptive smoothing approach are studied in depth.