We present an on-chip, widefield fluorescence microscope, which consists of a diffuser placed a few millimeters away from a traditional image sensor. The diffuser replaces the optics of a microscope, resulting in a compact and easy-to-assemble system with a practical working distance of over 1.5 mm. Furthermore, the diffuser encodes volumetric information, enabling refocusability in post-processing and three-dimensional (3D) imaging of sparse samples from a single acquisition. Reconstruction of images from the raw data requires a precise model of the system, so we introduce a practical calibration scheme and a physics-based forward model to efficiently account for the spatially-varying point spread function (PSF). To improve performance in low-light, we propose a random microlens diffuser, which consists of many small lenslets randomly placed on the mask surface and yields PSFs that are robust to noise. We build an experimental prototype and demonstrate our system on both planar and 3D samples.