Multilayer networks allow one to represent diverse and coupled connectivity
patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise
in many applications and which are difficult or awkward to incorporate into
standard network representations. In the study of multilayer networks, it is
important to investigate mesoscale (i.e., intermediate-scale) structures, such
as dense sets of nodes known as communities, to discover network features that
are not apparent at the microscale or the macroscale. The ill-defined nature of
mesoscale structure and its ubiquity in empirical networks make it crucial to
develop generative models that can produce the features that one encounters in
empirical networks. Key purposes of such generative models include generating
synthetic networks with empirical properties of interest, benchmarking
mesoscale-detection methods and algorithms, and inferring structure in
empirical multilayer networks. In this paper, we introduce a framework for the
construction of generative models for mesoscale structures in multilayer
networks. Our framework provides a standardized set of generative models,
together with an associated set of principles from which they are derived, for
studies of mesoscale structures in multilayer networks. It unifies and
generalizes many existing models for mesoscale structures in fully-ordered
(e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can
also use it to construct generative models for mesoscale structures in
partially-ordered multilayer networks (e.g., networks that are both temporal
and multiplex). Our framework has the ability to produce many features of
empirical multilayer networks, and it explicitly incorporates a user-specified
dependency structure between layers.