This paper builds a model that examines firm heterogeneity across two dimensions: productivity and quality. We show that when firms are able to choose their input quality and there exists a negative relationship between a firm's product quality and their marginal cost, this can lead to a non-unimodal distribution of quality across firms. Trade liberalization, represented by reductions in trade costs, and stronger vertical linkages, represented by an increase in the cost share of intermediate goods, shift the distribution of firms towards the modes of the distribution, which we call quality polarization. With this approach, we are able to explain empirical trade patterns relating to firm size, prices, and quality of exported goods.