Data quality problems are a large threat in data science. In this paper, we propose a data-cleaning autoencoder capable of near-automatic data quality improvement. It learns the structure and dependencies in the data and uses it as evidence to identify and correct doubtful values. We apply a probabilistic database approach to represent weak and strong evidence for attribute value repairs. A theoretical framework is provided, and experiments show that it can remove significant amounts of noise (i.e., data quality problems) from categorical and numeric probabilistic data. Our method does not require clean data. We do, however, show that manually cleaning a small fraction of the data significantly improves performance.