Black-box optimization formulations for biological sequence design have drawn recent attention due to their promising potential impact on the pharmaceutical industry. In this work, we propose to unify two seemingly distinct worlds – likelihood-free inference and black-box sequence design, under one probabilistic framework. In tandem, we provide a recipe for constructing various sequence design methods based on this framework. We show how previous drug discovery approaches can be “reinvented” in our framework, and further propose new probabilistic sequence design algorithms. Extensive experiments illustrate the benefits of the proposed methodology.