Trumpets: Injective Flows for Inference and Inverse Problems

TL;DR

Trumpets are a new class of injective generative models that extend normalizing flows, enabling faster training and effective Bayesian inference for inverse problems like image reconstruction.

Contribution

Introduction of Trumpets, a novel injective flow model that trains faster than standard flows and supports efficient Bayesian inference and uncertainty quantification.

Findings

Trumpets train orders of magnitude faster than standard flows.

They produce high-quality samples comparable or better than existing methods.

Trumpet priors improve image reconstruction quality and speed in inverse problems.

Abstract

We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space.