During the last few years, i-vectors have become an important component in most state-of-the-art speaker recognition systems. Ivector extraction is based on an assumption that GMM supervectors reside on a low dimensional space, which is modeled using Factor Analysis. In this paper we replace the above assumption with an assumption that the GMM supervectors reside on a low dimensional manifold and propose to use Diffusion Maps to learn that manifold. The learnt manifold implies a mapping of spoken sessions into a modified i-vector space which we call d-vector space. D-vectors can further be processed using standard techniques such as LDA, WCCN, cosine distance scoring or Probabilistic Linear Discriminant Analysis (PLDA). We demonstrate the usefulness of our approach on the telephone core conditions of NIST 2010, and obtain significant error reduction.