Human emotions can be inferred from facial expressions. However, the annotations of facial expressions are often highly noisy in common emotion coding models, including categorical and dimensional ones. To reduce human labelling effort on multi-task labels, we introduce a new problem of facial emotion recognition with noisy multi-task annotations. For this new problem, we suggest a formulation from the point of joint distribution match view, which aims at learning more reliable correlations among raw facial images and multi-task labels, resulting in the reduction of noise influence. In our formulation, we exploit a new method to enable the emotion prediction and the joint distribution learning in a unified adversarial learning game. Evaluation throughout extensive experiments studies the real setups of the suggested new problem, as well as the clear superiority of the proposed method over the state-of-the-art competing methods on either the synthetic noisy labeled CIFAR-10 or practical noisy multi-task labeled RAF and AffectNet. The code is available at https://github.com/sanweiliti/noisyFER.