Light-sheet microscopy is used extensively in developmental biology and neuroscience. One limitation of this approach is that absorption and scattering produces shadows in the illuminating light sheet, resulting in stripe artifacts. Here, we introduce diffuse light-sheet microscopes that use a line diffuser to randomize the light propagation within the image plane, allowing the light sheets to reform after obstacles. We incorporate diffuse light sheets in two existing configurations: selective plane illumination microscopy in which the sample is illuminated with a static sheet of light, and digitally scanned light sheet (DSLS) in which a thin Gaussian beam is scanned across the image plane during each acquisition. We compare diffuse light-sheet microscopes to their conventional counterparts for calcium imaging of neural activity in larval zebrafish. We show that stripe artifacts can cast deep shadows that conceal some neurons, and that the stripes can flicker, producing spurious signals that could be interpreted as biological activity. Diffuse light-sheets mitigate these problems, illuminating the blind spots produced by stripes and removing artifacts produced by the stripes' movements. The upgrade to diffuse light sheets is simple and inexpensive, especially in the case of DSLS, where it requires the addition of one optical element.