In many problems in machine learning there exist relations between data collections from different modalities. The purpose of multi-modal learning algorithms is to efficiently use the information present in different modalities when solving multi-modal retrieval problems. In this work, a multi-modal representation learning algorithm is proposed, which is based on nonlinear dimensionality reduction. Compared to linear dimensionality reduction methods, nonlinear methods provide more flexible representations especially when there is high discrepancy between the structures of different modalities. In this work, we propose to align different modalities by mapping same-class training data from different modalities to nearby coordinates, while we also learn a Lipschitz-continuous interpolation function that generalizes the learnt representation to the whole data space. Experiments in image-text retrieval applications show that the proposed method yields high performance when compared to multi-modal learning methods in the literature.