Quantitative item models are item structures that may be expressed in terms of mathematical variables and constraints. An item model may be developed as a computer program for which large numbers of items are automatically generated. Item models can be used to produce large numbers of items for use in traditional, large-scale assessments. But they have potential for use in other areas as well, including diagnostic assessment. In this report, I first review research on diagnostic assessment and then discuss how approaches to diagnostic assessment can inform the design of diagnostic item models.