Many speech processing methods based on deep learning require an automatic and differentiable audio metric for the loss function. The DPAM approach of Manocha et al. learns a full-reference metric trained directly on human judgments, and thus correlates well with human perception. However, it requires a large number of human annotations and does not generalize well outside the range of perturbations on which it was trained. This paper introduces CDPAM – a metric that builds on and advances DPAM. The primary improvement is to combine contrastive learning and multi-dimensional representations to build robust models from limited data. In addition, we collect human judgments on triplet comparisons to improve generalization to a broader range of audio perturbations. CDPAM correlates well with human responses across nine varied datasets. We also show that adding this metric to existing speech synthesis and enhancement methods yields significant improvement, as measured by objective and subjective tests.