An optical diffuser is an element that scatters light and is commonly used to soften or shape illumination. In this paper, we propose a novel depth estimation method that places a diffuser in the scene prior to image capture. We call this approach depth-from-diffusion (DFDiff). We show that DFDiff is analogous to conventional depth-from-defocus (DFD), where the scatter angle of the diffuser determines the effective aperture of the system. The main benefit of DFDiff is that while DFD requires very large apertures to improve depth sensitivity, DFDiff only requires an increase in the diffusion angle - a much less expensive proposition. We perform a detailed analysis of the image formation properties of a DFDiff system, and show a variety of examples demonstrating greater precision in depth estimation when using DFDiff.