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Psychometric functions typically characterize binary sensory decisions along a single stimulus dimension. However, real-life sensory tasks vary along a greater variety of dimensions (e.g. color, contrast and luminance for visual stimuli). Approaches to characterizing high-dimensional sensory spaces either require strong parametric assumptions about these additional contextual dimensions, or fail to leverage known properties of classical psychometric curves. We overcome both limitations by introducing a semi-parametric model of sensory discrimination that applies traditional psychophysical models along a stimulus intensity dimension, but puts Gaussian process (GP) priors on the parameters of these models with respect to the remaining dimensions. By combining the flexibility of the GP with the deep literature on parametric psychophysics, our semi-parametric models achieve good performance with much less data than baselines on both synthetic and real-world, high-dimensional psychophysics datasets. We additionally show strong performance in a Bayesian active learning setting, and present a novel active learning paradigm for the semi-parametric model.