Poor access to eye care is a major global challenge that could be ameliorated by low-cost, portable, and easy-to-use diagnostic technologies. Diffuser-based imaging has the potential to enable inexpensive, compact optical systems that can reconstruct a focused image of an object over a range of defocus errors. Here, we present a diffuser-based computational funduscope that reconstructs important clinical features of a model eye. Compared to existing diffuser-imager architectures, our system features an infinite-conjugate design by relaying the ocular lens onto the diffuser. This offers shift-invariance across a wide field-of-view (FOV) and an invariant magnification across an extended depth range. Experimentally, we demonstrate fundus image reconstruction over a 33° FOV and robustness to ±4D refractive error using a constant point-spread-function. Combined with diffuser-based wavefront sensing, this technology could enable combined ocular aberrometry and funduscopic screening through a single diffuser sensor.