We describe a machine learning technique for reconstructing image sequences rendered using Monte Carlo methods. Our primary focus is on reconstruction of global illumination with extremely low sampling budgets at interactive rates. Motivated by recent advances in image restoration with deep convolutional networks, we propose a variant of these networks better suited to the class of noise present in Monte Carlo rendering. We allow for much larger pixel neighborhoods to be taken into account, while also improving execution speed by an order of magnitude. Our primary contribution is the addition of recurrent connections to the network in order to drastically improve temporal stability for sequences of sparsely sampled input images. Our method also has the desirable property of automatically modeling relationships based on auxiliary per-pixel input channels, such as depth and normals. We show significantly higher quality results compared to existing methods that run at comparable speeds, and furthermore argue a clear path for making our method run at realtime rates in the near future