Neural networks are vulnerable to data inference attacks, including the membership inference attack, the model inversion attack, and the attribute inference attack. In this paper, we proposePurifierto defend against membership inference attacks by quantifying the differences between dataset members and non-members in three dimensions: individual shape, statistical distribution, and prediction label.Purifierinvolves transforming the confidence scores produced by the target classifier, resulting in purified confidence scores that are indistinguishable across the dimensions above. We conduct experiments on widely-used datasets and models. The results show thatPurifieroffers robust defense against membership inference attacks with superior efficacy compared to prior defense techniques while maintaining minimal utility degradation (e.g., less than 0.7% classification accuracy drop of most datasets). Additionally, our extended experiments explore the effectiveness ofPurifierin defending against the model inversion attack and the attribute inference attack.