Unsupervised learning of feature representations is a challenging yet important problem for analyzing a large collection of multimedia data that do not have semantic labels. Recently proposed neural network-based unsupervised learning approaches have succeeded in obtaining features appropriate for classification of multimedia data. However, unsupervised learning of feature representations adapted to content-based matching, comparison, or retrieval of multimedia data has not been explored well. To obtain such retrieval-adapted features, we introduce the idea of combining diffusion distance on a feature manifold with neural network-based unsupervised feature learning. This idea is realized as a novel algorithm called DeepDiffusion (DD). DD simultaneously optimizes two components, a feature embedding by a deep neural network and a distance metric that leverages diffusion on a latent feature manifold, together. DD relies on its loss function but not encoder architecture. It can thus be applied to diverse multimedia data types with their respective encoder architectures. Experimental evaluation using 3D shapes and 2D images demonstrates versatility as well as high accuracy of the DD algorithm. Code is available at https://github.com/takahikof/DeepDiffusion