This paper presents a novel metric learning approach to address the performance gap between normal and silent speech in visual speech recognition (VSR). The difference in lip movements between the two poses a challenge for existing VSR models, which exhibit degraded accuracy when applied to silent speech. To solve this issue and tackle the scarcity of training data for silent speech, we propose to leverage the shared literal content between normal and silent speech and present a metric learning approach based on visemes. Specifically, we aim to map the input of two speech types close to each other in a latent space if they have similar viseme representations. By minimizing the Kullback-Leibler divergence of the predicted viseme probability distributions between and within the two speech types, our model effectively learns and predicts viseme identities. Our evaluation demonstrates that our method improves the accuracy of silent VSR, even when limited training data is available.