Most deep learning approaches to comprehensive semantic modeling of 3D indoor spaces require costly dense annotations in the 3D domain. In this work, we explore a central 3D scene modeling task, namely, semantic scene reconstruction, using a fully self-supervised approach. To this end, we design a trainable model that employs both incomplete 3D reconstructions and their corresponding source RGB-D images, fusing cross-domain features into volumetric embeddings to predict complete 3D geometry, color, and semantics. Our key technical innovation is to leverage differentiable rendering of color and semantics, using the observed RGB images and a generic semantic segmentation model as color and semantics supervision, respectively. We additionally develop a method to synthesize an augmented set of virtual training views complementing the original real captures, enabling more efficient self-supervision for semantics. In this work we propose an end-to-end trainable solution jointly addressing geometry completion, colorization, and semantic mapping from a few RGB-D images, without 3D or 2D ground-truth. Our method is the first, to our knowledge, fully self-supervised method addressing completion and semantic segmentation of real-world 3D scans. It performs comparably well with the 3D supervised baselines, surpasses baselines with 2D supervision on real datasets, and generalizes well to unseen scenes.