Proximal Residual Flows for Bayesian Inverse Problems
This work addresses Bayesian inverse problems for applications like imaging or signal processing, but it appears incremental as it builds on existing normalizing flow methods with a specific architectural modification.
The authors tackled the problem of generative modeling and posterior reconstruction in Bayesian inverse problems by introducing proximal residual flows, a new normalizing flow architecture that ensures invertibility through proximal neural networks, and demonstrated its performance on numerical examples.
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows. Based on the fact, that proximal neural networks are by definition averaged operators, we ensure invertibility of certain residual blocks. Moreover, we extend the architecture to conditional proximal residual flows for posterior reconstruction within Bayesian inverse problems. We demonstrate the performance of proximal residual flows on numerical examples.