In this work, we propose deep latent space clustering for speaker diarization using generative adversarial network (GAN) backprojection with the help of an encoder network. The proposed diarization system is trained jointly with GAN loss, latent variable recovery loss, and a clustering-specific loss. It uses x-vector speaker embeddings at the input, while the latent variables are sampled from a combination of continuous random variables and discrete one-hot encoded variables using the original speaker labels. We benchmark our proposed system on the AMI meeting corpus, and two child-clinician interaction corpora (ADOS and BOSCC) from the autism diagnosis domain. ADOS and BOSCC contain diagnostic and treatment outcome sessions respectively obtained in clinical settings for verbal children and adolescents with autism. Experimental results show that our proposed system significantly outperform the state-of-the-art x-vector based diarization system on these databases. Further, we perform embedding fusion with x-vectors to achieve a relative DER improvement of 31%, 36% and 49% on AMI eval, ADOS and BOSCC corpora respectively, when compared to the x-vector baseline using oracle speech segmentation.