  A flexible multimode fiber is an exceptionally efficient tool for in vivo
deep tissue imaging. Recent advances in compressive multimode fiber sensing
allow for imaging with sub-diffraction spatial resolution and sub-Nyquist
speed. At present, the technology is limited to imaging in a two-dimensional
(2D) plane near the fiber distal facet while in real applications it is very
important to visualize three-dimensional (3D) structures. Here we propose a new
approach for fast sub-diffraction 3D imaging through a multimode fiber by using
a single 2D scan, speckle illumination, and bucket detection. We experimentally
demonstrate precise image plane location as well as 3D imaging of samples with
various scattering coefficients. The full width at half maximum (FWHM) of the
point spread function along the axial direction is 3 times smaller than the
diffraction limit. Our study grants depth-resolving capacity to ultra-thin
super-resolution fiber endoscopes for life science and medical applications.
