Progress in probabilistic generative models has accelerated, developing richer models with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference. However, there has been limited progress in models that capture causal relationships, for example, how individual genetic factors cause major human diseases. In this work, we focus on two challenges in particular: How do we build richer causal models, which can capture highly nonlinear relationships and interactions between multiple causes? How do we adjust for latent confounders, which are variables influencing both cause and effect and which prevent learning of causal relationships? To address these challenges, we synthesize ideas from causality and modern probabilistic modeling. For the first, we describe implicit causal models, a class of causal models that leverages neural architectures with an implicit density. For the second, we describe an implicit causal model that adjusts for confounders by sharing strength across examples. In experiments, we scale Bayesian inference on up to a billion genetic measurements. We achieve state of the art accuracy for identifying causal factors: we significantly outperform the second best result by an absolute difference of 15-45.3%.