Thoroughly understanding how energy consumption is disaggregated into individual appliances can help reduce household expenses, integrate renewable sources of energy, and lead to efficient use of energy. In this work, we propose a deep latent generative model based on variational recurrent neural networks (VRNNs) for energy disaggregation. Our model jointly disaggregates the aggregated energy signal into individual appliance signals, achieving superior performance when compared to the state-of-the-art models for energy disaggregation, yielding a 29% and 41% performance improvement on two energy datasets, respectively, without explicitly encoding temporal/contextual information or heuristics. Our model also achieves better prediction performance on low-power appliances, paving the way for a more nuanced disaggregation model. The structured output prediction in our model helps in accurately discerning which appliance(s) contribute to the aggregated power consumption, thus providing a more useful and meaningful disaggregation model.