Depth completion upgrades sparse depth measurements into dense depth maps guided by a conventional image. Existing methods for this highly ill-posed task operate in tightly constrained settings, and tend to struggle when applied to images outside the training domain, as well as when the available depth measurements are sparse, irregularly distributed, or of varying density. Inspired by recent advances in monocular depth estimation, we reframe depth completion as image-conditional depth map generation guided by a sparse set of measurements. Our method, Marigold-DC, builds on a pretrained latent diffusion model (LDM) for depth estimation and injects the depth observations as test-time guidance, via an optimization scheme that runs in tandem with the iterative inference of denoising diffusion. The method exhibits excellent zero-shot generalization across a diverse range of environments and handles even extremely sparse guidance effectively. Our results suggest that contemporary monodepth priors greatly robustify depth completion: it may be better to view the task as recovering dense depth from (dense) image pixels, guided by sparse depth; rather than as inpainting (sparse) depth, guided by an image.