Trumpets: Injective Flows for Inference and Inverse Problems
This work addresses computational bottlenecks in generative modeling for researchers and practitioners, offering a faster alternative to standard flows with applications in inverse problems like compressive sensing.
The authors tackled the problem of slow training and inference in generative models by proposing Trumpets, injective flows that generalize invertible normalizing flows, which train orders of magnitude faster while maintaining or improving sample quality and enabling efficient Bayesian inference for tasks like image reconstruction, outperforming baselines in quality and speed.
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.