Document-level relation extraction aims to categorize the association between any two entities within a document. We find that previous methods for document-level relation extraction are ineffective in exploiting the full potential of large amounts of training data with varied noise levels. For example, in the ReDocRED benchmark dataset, state-of-the-art methods trained on the large-scale, lower-quality, distantly supervised training data generally do not perform better than those trained solely on the smaller, high-quality, human-annotated training data. To unlock the full potential of large-scale noisy training data for document-level relation extraction, we propose TTM-RE, a novel approach that integrates a trainable memory module, known as the Token Turing Machine, with a noisy-robust loss function that accounts for the positive-unlabeled setting. The trainable memory module enhances knowledge extraction from the large-scale noisy training dataset through an explicit learning of the memory tokens and a soft integration of the learned memory tokens into the input representation, thereby improving the model's effectiveness for the final relation classification. Extensive experiments on ReDocRED, a benchmark dataset for document-level relation extraction, reveal that TTM-RE achieves state-of-the-art performance (with an absolute F1 score improvement of over 3%). Ablation studies further illustrate the superiority of TTM-RE in other domains (the ChemDisGene dataset in the biomedical domain) and under highly unlabeled settings.