Multi-contrast MRI and multi-parametric maps provide complementary qualitative and quantitative information for disease diagnosis. However, due to limited scan time, a full array of images is often unavailable in practice. To provide both qualitative weighted images and quantitative maps using a weighted-only or mapping-only acquisition, in this work, we propose to perform bidirectional translation between conventional weighted images and parametric maps. We developed a combined training strategy of two convolutional neural networks with cycle consistency loss. Our preliminary results show that the proposed method can translate between contrast-weighted images and quantitative maps with high quality and fidelity.