Wavefront sensing is typically accomplished with a Shack-Hartmann wavefront sensor (SHWS), where a CCD or CMOS is placed at the focal plane of a periodic, microfabricated lenslet array. Tracking the displacement of the resulting spots in the presence of an aberrated wavefront yields measurement of the relative wavefront introduced. A SHWS has a fundamental tradeoff between sensitivity and range, determined by the pitch and focal length of its lenslet array, such that the number of resolvable tilts is a constant. Recently, diffuser wavefront sensing (DWS) has been demonstrated by measuring the lateral shift of a coherent speckle pattern using the concept of the diffuser memory effect. Here we demonstrate that tracking distortions of the non-periodic caustic pattern produced by a holographic diffuser allows accurate autorefraction of a model eye with a number of resolvable tilts that extends beyond the fundamental limit of a SHWS. Using a multi-level Demon’s image registration algorithm, we are able to demonstrate that a DWS demonstrates a 2.5x increase in number of resolvable prescriptions as compared to a conventional SHWS while maintaining acceptable accuracy and repeatability for eyeglass prescriptions. We evaluate the performance of a DWS and SHWS in parallel with a coherent laser diode without (LD) and with a laser speckle reducer (LD+LSR), and an incoherent light-emitting diode (LED), demonstrating caustic-tracking is compatible with coherent and incoherent sources. Additionally, the DWS diffuser costs 40x less than a SHWS lenslet array, enabling affordable large-dynamic range autorefraction without moving parts.