In display advertising, predicting the conversion rate (CVR), meaning the probability that a user takes a predefined action on an advertiser’s website, is a fundamental task for estimating the value of displaying an advertisement to a user. There are two main challenges in CVR prediction due to delayed feedback. First, some positive labels are not correctly observed in training data because some conversions do not occur immediately after a click. Second, delay mechanisms are not uniform among instances, meaning some positive feedback are much more frequently observed than others. It is widely acknowledged that these problems lead to severe bias in CVR prediction. To overcome these challenges, we propose two unbiased estimators: one for CVR prediction and the other for bias estimation. Subsequently, we propose a dual learning algorithm in which a CVR predictor and a bias estimator are trained in alternating fashion using only observable conversions. The proposed algorithm is the first of its kind to address the two major challenges in a theoretically sophisticated manner. Empirical evaluations using synthetic datasets demonstrate the practical value of the proposed approach.