Nowadays, web data is often used to train a dialogue system. However, noises in web data can disturb the training process, as well as can impact the performance. Consequently, dialogue models tend to be brittle when receiving noisy inputs during the inference. This paper proposes a novel framework, Multi-Path Training (MPT), for training a robust dialogue response generation system. MPT improves the robustness to the noisy training data and the noisy inference queries using three paths. Experimental results show MPT can outperform baselines using the same backbone model, and also prove MPT can improve the robustness to the noise in both the training and inference stage.