Proximal Residual Flows for Bayesian Inverse Problems

TL;DR

This paper introduces proximal residual flows, a novel invertible neural network architecture based on proximal operators, designed for improved posterior reconstruction in Bayesian inverse problems, demonstrating promising numerical results.

Contribution

The paper proposes proximal residual flows, ensuring invertibility via proximal neural networks, and extends this architecture to conditional flows for Bayesian inverse problems.

Findings

Effective posterior reconstruction demonstrated on numerical examples

Proximal residual flows ensure invertibility through averaged operator properties

Extension to conditional flows enhances Bayesian inverse problem solutions

Abstract

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.