Abstract: Future video prediction is an ill-posed Computer Vision problem that recently received much attention. Its main challenges are the high variability in video content, the propagation of errors through time, and the non-specificity of the future frames: given a sequence of past frames there is a continuous distribution of possible futures. This work introduces bijective Gated Recurrent Units, a double mapping between the input and output of a GRU layer. This allows for recurrent auto-encoders with state sharing between encoder and decoder, stratifying the sequence representation and helping to prevent capacity problems. We show how with this topology only the encoder or decoder needs to be applied for input encoding and prediction, respectively. This reduces the computational cost and avoids re-encoding the predictions when generating a sequence of frames, mitigating the propagation of errors. Furthermore, it is possible to remove layers from an already trained model, giving an insight to the role performed by each layer and making the model more explainable. We evaluate our approach on three video datasets, outperforming state of the art prediction results on MMNIST and UCF101, and obtaining competitive results on KTH with 2 and 3 times less memory usage and computational cost than the best scored approach.