Degeneration of intervertebral discs (IVDs) is correlated with low back pain, but conventional MRI fails to capture early signs of degeneration. Quantitative MRI (qMRI) is sensitive to early degenerative biochemical changes but suffers from long acquisition times. We present a recurrent encoder-decoder architecture that predicts fully sampled IVD T2 maps from spatially and temporally undersampled qMRI echos. The network allows for up to eightfold reduction in acquisition time while exhibiting strong correlation to ground truth maps, maintaining fidelity to T2 values, and retaining textures. With further development, this network can make qMRI a more regular part of lumbar spine imaging.