In order to improve signal-to-noise ratio (SNR) and contrast-to-noise ratio, this paper introduces a local variance-controlled forward-and-backward (LVCFAB) diffusion algorithm for edge enhancement and noise reduction. In our algorithm, an alternative FAB diffusion algorithm is proposed. The results for the alternative FAB algorithm show better algorithm behavior than other existing diffusion FAB approaches. Furthermore, two distinct discontinuity measures and the alternative FAB diffusion are incorporated into a LVCFAB diffusion algorithm, where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images. This LVC mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity. Qualitative experiments, based on general digital images and magnetic resonance images, show significant improvements when the LVCFAB diffusion algorithm is used versus the existing anisotropic diffusion and the previous FAB diffusion algorithms for enhancing edge features and improving image contrast. Quantitative analyses, based on peak SNR, confirm the superiority of the proposed LVCFAB diffusion algorithm.