An invertible generative model for forward and inverse problems
This work addresses conditional generative modeling for Bayesian inverse problems, but it appears incremental as it builds on existing triangular flow methods.
The paper tackles the problem of solving forward and inverse problems by developing an invertible generative model using triangular normalizing flows, enabling both simulation and inference, and demonstrates its functionality through numerical examples.
We formulate the inverse problem in a Bayesian framework and aim to train a generative model that allows us to simulate (i.e., sample from the likelihood) and do inference (i.e., sample from the posterior). We review the use of triangular normalizing flows for conditional sampling in this context and show how to combine two such triangular maps (an upper and a lower one) in to one invertible mapping that can be used for simulation and inference. We work out several useful properties of this invertible generative model and propose a possible training loss for training the map directly. We illustrate the workings of this new approach to conditional generative modeling numerically on a few stylized examples.