Sequential recommenders that are trained on implicit feedback are usually learned as a multi-class classification task through softmax-based loss functions on one-hot class labels. However, one-hot training labels are sparse and may lead to biased training and sub-optimal performance. Dense, soft labels have been shown to help improve recommendation performance. But how to generate high-quality and confident soft labels from noisy sequential interactions between users and items is still an open question. We propose a new learning framework for sequential recommenders, CSRec, which introduces confident soft labels to provide robust guidance when learning from user-item interactions. CSRec contains a teacher module that generates high-quality and confident soft labels and a student module that acts as the target recommender and is trained on the combination of dense, soft labels and sparse, one-hot labels. We propose and compare three approaches to constructing the teacher module: (i) model-level, (ii) data-level, and (iii) training-level. To evaluate the effectiveness and generalization ability of CSRec, we conduct experiments using various state-of-the-art sequential recommendation models as the target student module on four benchmark datasets. Our experimental results demonstrate that CSRec is effective in training better performing sequential recommenders.