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We present CoGS, a novel method for the style-conditioned, sketch-driven synthesis of images. CoGS enables exploration of diverse appearance possibilities for a given sketched object, enabling decoupled control over the structure and the appearance of the output. Coarse-grained control over object structure and appearance are enabled via an input sketch and an exemplar "style" conditioning image to a transformer-based sketch and style encoder to generate a discrete codebook representation. We map the codebook representation into a metric space, enabling fine-grained control over selection and interpolation between multiple synthesis options before generating the image via a vector quantized GAN (VQGAN) decoder. Our framework thereby unifies search and synthesis tasks, in that a sketch and style pair may be used to run an initial synthesis which may be refined via combination with similar results in a search corpus to produce an image more closely matching the user's intent. We show that our model, trained on the 125 object classes of our newly created Pseudosketches dataset, is capable of producing a diverse gamut of semantic content and appearance styles.