We propose a hierarchical protein backbone generative model that separates coarse and fine-grained details. Our approach called LSD consists of two stages: sampling latents which are decoded into a contact map then sampling atomic coordinates conditioned on the contact map. LSD allows new ways to control protein generation towards desirable properties while scaling to large datasets. In particular, the AlphaFold DataBase (AFDB) is appealing due as its diverse structure topologies but suffers from poor designability. We train LSD on AFDB and show latent diffusion guidance towards AlphaFold2 Predicted Alignment Error and long range contacts can explicitly balance designability, diversity, and noveltys in the generated samples. Our results are competitive with structure diffusion models and outperforms prior latent diffusion models.