It is difficult to apply well-formulated model-based noise adaptation approaches to Deep Neural Network (DNN) due to the lack of interpretability of the model parameters. In this paper, we propose incorporating a generative front-end layer (GFL), which is parameterised by Gaussian Mixture Model (GMM), into the DNN. A GFL can be easily adapted to different noise conditions by applying the model-based Vector Taylor Series (VTS) to the underlying GMM. We show that incorporating a GFL to DNN yields 12.1% relative improvement over a baseline multi-condition DNN. We also show that the proposed system performs significantly better than the noise aware training method, where the per-utterance estimated noise parameters are appended to the acoustic features.