In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible neurobiologically-motivated algorithm that progressively refines latent state feature maps in order to dynamically form a more accurate internal representation/reconstruction model of natural images. The performance of the resulting sensory processing system is evaluated on complex datasets such as Color-MNIST, CIFAR-10, and Street House View Numbers (SVHN). We study the effectiveness of our brain-inspired model on the tasks of reconstruction and image denoising and find that it is competitive with convolutional auto-encoding systems trained by backpropagation of errors and outperforms them with respect to out-of-distribution reconstruction (including the full 90k CINIC-10 test set).