Neurons in the dorsal subregion of the medial superior temporal (MSTd) area respond to large, complex patterns of retinal flow, implying a role in the analysis of self-motion. Some neurons are selective for the expanding radial motion that occurs as an observer moves through the environment (heading), and computational models can account for this finding. However, ample evidence suggests that MSTd neurons may exhibit a continuum of visual response selectivity to large-field motion stimuli, but the underlying computational principles by which these response properties are derived remain poorly understood. Here we describe a computational model of MSTd based on the hypothesis that neurons in MSTd efficiently encode the continuum of large-field retinal flow patterns on the basis of inputs received from neurons in MT, with receptive fields that resemble basis vectors recovered with nonnegative matrix factorization (NMF). These assumptions are sufficient to quantitatively simulate neurophysiological response properties of MSTd cells such as radial, circular, and spiral motion tuning, suggesting that these properties might simply be a by-product of MSTd neurons performing dimensionality reduction on their inputs. At the population level, model MSTd accurately predicts heading using a sparse distributed code, consistent with the idea that biological MSTd might operate in a sparseness regime well-suited to efficiently encode a number of self-motion variables. The present work provides an alternative to the template-model view of MSTd, and offers a biologically plausible account of the receptive field structure across a wide range of visual response properties in MSTd.