Implicit discourse relation recognition (IDRR) is a challenging but crucial task in discourse analysis. Most existing methods train multiple models to predict multi-level labels independently, while ignoring the dependence between hierarchically structured labels. In this paper, we consider multi-level IDRR as a conditional label sequence generation task and propose a Label Dependence-aware Sequence Generation Model (LDSGM) for it. Specifically, we first design a label attentive encoder to learn the global representation of an input instance and its level-specific contexts, where the label dependence is integrated to obtain better label embeddings. Then, we employ a label sequence decoder to output the predicted labels in a top-down manner, where the predicted higher-level labels are directly used to guide the label prediction at the current level. We further develop a mutual learning enhanced training method to exploit the label dependence in a bottom-up direction, which is captured by an auxiliary decoder introduced during training. Experimental results on the PDTB dataset show that our model achieves the state-of-the-art performance on multi-level IDRR. We release our code at https://github.com/nlpersECJTU/LDSGM.