  Normalizing flows model probability distributions by learning invertible
transformations that transfer a simple distribution into complex distributions.
Since the architecture of ResNet-based normalizing flows is more flexible than
that of coupling-based models, ResNet-based normalizing flows have been widely
studied in recent years. Despite their architectural flexibility, it is
well-known that the current ResNet-based models suffer from constrained
Lipschitz constants. In this paper, we propose the monotone formulation to
overcome the issue of the Lipschitz constants using monotone operators and
provide an in-depth theoretical analysis. Furthermore, we construct an
activation function called Concatenated Pila (CPila) to improve gradient flow.
The resulting model, Monotone Flows, exhibits an excellent performance on
multiple density estimation benchmarks (MNIST, CIFAR-10, ImageNet32,
ImageNet64). Code is available at https://github.com/mlvlab/MonotoneFlows.
