Recovering spatially-varying materials from a single photograph of a surface is inherently ill-posed, making the direct application of a gradient descent on the reflectance parameters prone to poor minima. Recent methods leverage deep learning either by directly regressing reflectance parameters using feed-forward neural networks or by learning a latent space of SVBRDFs using encoder-decoder or generative adversarial networks followed by a gradient-based optimization in latent space. The former is fast but does not account for the likelihood of the prediction, i.e., how well the resulting reflectance explains the input image. The latter provides a strong prior on the space of spatially-varying materials, but this prior can hinder the reconstruction of images that are too different from the training data. Our method combines the strengths of both approaches. We optimize reflectance parameters to best reconstruct the input image using a recurrent neural network, which iteratively predicts how to update the reflectance parameters given the gradient of the reconstruction likelihood. By combining a learned prior with a likelihood measure, our approach provides a maximum a posteriori estimate of the SVBRDF. Our evaluation shows that this learned gradient-descent method achieves state-of-the-art performance for SVBRDF estimation on synthetic and real images.@en