Few-shot deep learning is a topical challenge area for scaling visual recognition to open ended growth of unseen new classes with limited labeled examples. A promising approach is based on metric learning, which trains a deep embedding to support image similarity matching. Our insight is that effective general purpose matching requires non-linear comparison of features at multiple abstraction levels. We thus propose a new deep comparison network comprised of embedding and relation modules that learn multiple non-linear distance metrics based on different levels of features simultaneously. Furthermore, to reduce over-fitting and enable the use of deeper embeddings, we represent images as distributions rather than vectors via learning parameterized Gaussian noise regularization. The resulting network achieves excellent performance on both miniImageNet and tieredImageNet.