The photo-sketch matching problem is challenging because the modality gap between a photo and a sketch is very large. This work features a novel approach to the use of an intermediate latent space between the two modalities that circumvents the problem of modality gap for face photo-sketch recognition. To set up a stable homogenous latent space between a photo and a sketch that is effective for matching, we utilize a bidirectional (photo → sketch and sketch → photo) collaborative synthesis network and equip the latent space with rich representation power. To provide rich representation power, we employ StyleGAN architectures, such as StyleGAN and StyleGAN2. The proposed latent space equipped with rich representation power enables us to conduct accurate matching because we can effectively align the distributions of the two modalities in the latent space. In addition, to resolve the problem of insufficient paired photo/sketch samples for training, we introduce a three-step training scheme. Extensive evaluation on a public composite face sketch database confirms superior performance of the proposed approach compared to existing state-of-the-art methods. The proposed methodology can be employed in matching other modality pairs.