Trumpets: Injective Flows for Inference and 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.

16 pages

References in corpus (5)

• GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
• NICE: Non-linear Independent Components Estimation
• Towards Principled Methods for Training Generative Adversarial Networks
• Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging
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Cited by in corpus (3)

• Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces
• Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows
• X2CT-FLOW: Maximum a posteriori reconstruction using a progressive flow-based deep generative model for ultra sparse-view computed tomography in ultra low-dose protocols