Estimating the motion of objects in depth is important for behavior and is strongly supported by binocular visual cues. To understand both how the brain should estimate motion in depth and how natural constraints shape and limit performance in two local 3D motion tasks, we develop image-computable ideal observers from a large number of binocular video clips created from a dataset of natural images. The observers spatiotemporally filter the videos and nonlinearly decode 3D motion from the filter responses. The optimal filters and decoder are dictated by the task-relevant image statistics and are specific to each task. Multiple findings emerge. First, two distinct filter subpopulations are spontaneously learned for each task. For 3D speed estimation, filters emerge for processing either changing disparities over time or interocular velocity differences, cues that are used by humans. For 3D direction estimation, filters emerge for discriminating either left–right or toward–away motion. Second, the filter responses, conditioned on the latent variable, are well-described as jointly Gaussian, and the covariance of the filter responses carries the information about the task-relevant latent variable. Quadratic combination is thus necessary for optimal decoding, which can be implemented by biologically plausible neural computations. Finally, the ideal observer yields nonobvious—and in some cases counterintuitive—patterns of performance like those exhibited by humans. Important characteristics of human 3D motion processing and estimation may therefore result from optimal information processing in the early visual system.