Audio-visual speech recognition (AVSR) provides a promising solution to ameliorate the noise-robustness of audio-only speech recognition with visual information. However, most existing efforts still focus on audio modality to improve robustness considering its dominance in AVSR task, with noise adaptation techniques such as front-end denoise processing. Though effective, these methods are usually faced with two practical challenges: 1) lack of sufficient labeled noisy audio-visual training data in some real-world scenarios and 2) less optimal model generality to unseen testing noises. In this work, we investigate the noise-invariant visual modality to strengthen robustness of AVSR, which can adapt to any testing noises while without dependence on noisy training data, a.k.a., unsupervised noise adaptation. Inspired by human perception mechanism, we propose a universal viseme-phoneme mapping (UniVPM) approach to implement modality transfer, which can restore clean audio from visual signals to enable speech recognition under any noisy conditions. Extensive experiments on public benchmarks LRS3 and LRS2 show that our approach achieves the state-of-the-art under various noisy as well as clean conditions. In addition, we also outperform previous state-of-the-arts on visual speech recognition task.