Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, leading to an efficiently invertible block with dense, triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We evaluate our method on some standard data sets and benchmark its full power for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.

This work addresses the task of non-blind image deconvolution. Motivated to keep up with the constant increase in image size, with megapixel images becoming the norm, we aim at pushing the limits of efficient FFT-based techniques. Based on an analysis of traditional and more recent learning-based methods, we generalize existing discriminative approaches by using more powerful regularization, based on convolutional neural networks. Additionally, we propose a simple, yet effective, boundary adjustment method that alleviates the problematic circular convolution assumption, which is necessary for FFT-based deconvolution. We evaluate our approach on two common non-blind deconvolution benchmarks and achieve state-of-the-art results even when including methods which are computationally considerably more expensive.