Cognitive diagnostic models (CDMs) have been a focus of research in recent years as a way to provide diagnostic information instead of a single test score on educational and psychological tests. CDM-based tests are designed to provide attribute profiles, or classifications of examinees that usually involve mastery or nonmastery, on each of the attributes measured by the test (Rupp, Templin, & Henson, 2010). As our knowledge of CDMs expands, there is likely to be a need for a way to link attribute profiles and observed test scores. The purpose of this brief report is to introduce and demonstrate a method for estimating an observed score distribution from an attribute profile. Although any CDM can be used with the proposed method, the authors chose the Log-Linear Cognitive Diagnostic Model (LCDM; Henson, Templin, & Willse, 2009) because many popular CDMs can be derived as special cases. The probability of a correct response to item i for an individual with an attribute profile a c is specified as