Abstract: 3D delineation of anatomical structures is a cardinal goal in medical imaging analysis. Prior to deep learning, statistical shape models that imposed anatomical constraints and produced high quality surfaces were a core technology. Prior to deep learning, statistical shape models that imposed anatomical constraints and produced high quality surfaces were a core technology. Today fully-convolutional networks (FCNs), while dominant, do not offer these capabilities. We present deep implicit statistical shape models (DISSMs), a new approach to delineation that marries the representation power of convolutional neural networks (CNNs) with the robustness of SSMs. DISSMs use a deep implicit surface representation to produce a compact and descriptive shape latent space that permits statistical models of anatomical variance. To reliably fit anatomically plausible shapes to an image, we introduce a novel rigid and non-rigid pose estimation pipeline that is modelled as a Markov decision process(MDP). We outline a training regime that includes inverted episodic training and a deep realization of marginal space learning (MSL). Intra-dataset experiments on the task of pathological liver segmentation demonstrate that DISSMs can perform more robustly than three leading FCN models, including nnU-Net: reducing the mean Hausdorff distance (HD) by 7.7-14.3mm and improving the worst case Dice-Sorensen coefficient (DSC) by 1.2-2.3%. More critically, cross-dataset experiments on a dataset directly reflecting clinical deployment scenarios demonstrate that DISSMs improve the mean DSC and HD by 3.5-5.9% and 12.3-24.5mm, respectively, and the worst-case DSC by 5.4-7.3%. These improvements are over and above any benefits from representing delineations with high-quality surface.