In this study, we present a novel semi-supervised generative model for multi-contrast MRI that synthesizes high-quality images without requiring large training sets of costly fully-sampled images of source or target contrasts. To do this, the proposed method introduces a selective loss expressed only in the available k-space coefficients, and further leverages randomized sampling trajectories across training subjects to effectively learn relationships between acquired and nonacquired k-space samples at all locations. Comprehensive experiments on multi-contrast brain images clearly demonstrate that the proposed method maintains equivalent performance to gold-standard model based on fully-supervised training, while alleviating undesirable dependency on large-scale fully-sampled MRI acquisitions.