Rapid advances in additive manufacturing and topology optimization enable unprecedented levels of design freedom for realizing complex structures. The challenge is that the increasing design freedom is accompanied by increasing complexity, such that it can become difficult for either computational algorithms or human designers alone to search these expansive design spaces effectively. Our goal is to establish an interactive design framework that is both data-driven and designer-guided so that human designers can work together with computational algorithms to search structural design spaces more effectively. The framework builds upon classical topology optimization techniques to build a library of designs for a class of problems. A conditional generative adversarial network (cGAN) is trained to establish a latent representation of the library and to support rapid exploration of candidate designs. The library of designs is clustered based on visual similarity. The user selects clusters with desirable features, and the underlying latent representation is manipulated to generate visually similar candidate designs with adjustable levels of diversity or similarity to the selected clusters. The framework enables designers to use their expertise and intuition to guide the algorithm towards promising solutions by screening designs quickly and eliminating clusters of designs that may not be desirable for reasons that are difficult to embed within the optimization itself but are recognizable and significant to a human designer (e.g., secondary functionality, aesthetics).