In open-domain Question Answering (QA) , dense retrieval is crucial for finding relevant passages for answer generation. Typically, contrastive learning is used to train a retrieval model that maps passages and queries to the same semantic space. The objective is to make similar ones closer and dissimilar ones further apart. However, training such a system is challenging due to the false negative issue, where relevant passages may be missed during data annotation. Hard negative sampling, which is commonly used to improve contrastive learning, can introduce more noise in training. This is because hard negatives are those closer to a given query, and thus more likely to be false negatives. To address this issue, we propose a novel contrastive confidence regularizer for Noise Contrastive Estimation (NCE)  loss, a commonly used loss for dense retrieval. Our analysis shows that the regularizer helps dense retrieval models be more robust against false negatives with a theoretical guarantee. Additionally, we propose a model-agnostic method to filter out noisy negative passages in the dataset, improving any downstream dense retrieval models. Through experiments on three datasets, we demonstrate that our method achieves better retrieval performance in comparison to existing state-of-the-art dense retrieval systems.