mlsanityData to 7 Oct 2026

Trumpets: Injective Flows for Inference and Inverse Problems

arXiv 2102.10461 ↗First posted 20 Feb 2021cs.LG cs.AI eess.SPcited by 36

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Abstract (arXiv)

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.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 24 of its 39 references that are in the map. First posted on arXiv 20 Feb 2021.

Builds on

24 of 39 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  5. 2016Density estimation using Real NVPcited by 2,029
  6. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  7. 2017Deep Image Priorcited by 1,097
  8. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  9. 2016Pixel Recurrent Neural Networkscited by 814
  10. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  11. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  12. 2019Neural Spline Flowscited by 590
12 more
  1. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  2. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
  3. 2017Compressed Sensing using Generative Modelscited by 337
  4. 2019Residual Flows for Invertible Generative Modelingcited by 256
  5. 2018i-RevNet: Deep Invertible Networkscited by 137
  6. 2020Flows for simultaneous manifold learning and density estimationcited by 117
  7. 2020Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximatorscited by 85
  8. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  9. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  10. 2020Regularized Autoencoders via Relaxed Injective Probability Flowcited by 23
  11. 2020Globally Injective ReLU Networkscited by 23
  12. 2020Normalizing Flows Across Dimensionscited by 19

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Citing papers per year: 2021: 5; 2022: 16; 2023: 8; 2024: 7.

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  1. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  2. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  3. 2021Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flowscited by 30
  4. 2022Diagnosing and Fixing Manifold Overfitting in Deep Generative Modelscited by 28
  5. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  6. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  7. 2023Lifting Architectural Constraints of Injective Flowscited by 17
  8. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  9. 2021Universal Joint Approximation of Manifolds and Densities by Simple Injective Flowscited by 13
  10. 2022Conditional Injective Flows for Bayesian Imagingcited by 13
  11. 2021Deep Bayesian inference for seismic imaging with taskscited by 12
  12. 2022VQ-Flows: Vector Quantized Local Normalizing Flowscited by 10
24 more
  1. 2023Injectivity of ReLU networks: perspectives from statistical physicscited by 10
  2. 2023Image Reconstruction without Explicit Priorscited by 8
  3. 2022Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spacescited by 6
  4. 2022Denoising Deep Generative Modelscited by 6
  5. 2022Nonlinear Isometric Manifold Learning for Injective Normalizing Flowscited by 5
  6. 2022Neural Implicit Manifold Learning for Topology-Aware Density Estimationcited by 5
  7. 2023Discovering Structure From Corruption for Unsupervised Image Reconstructioncited by 5
  8. 2022Principal Manifold Flowscited by 4
  9. 2022FunkNN: Neural Interpolation for Functional Generationcited by 4
  10. 2023Deep Injective Prior for Inverse Scatteringcited by 3
  11. 2023An Integral Projection-based Semantic Autoencoder for Zero-Shot Learningcited by 3
  12. 2022Accelerating Inverse Learning via Intelligent Localization with Exploratory Samplingcited by 2
  13. 2022Deep Variational Inverse Scatteringcited by 2
  14. 2024Analyzing Generative Models by Manifold Entropic Metricscited by 2
  15. 2024LoFi: Neural Local Fields for Scalable Image Reconstructioncited by 2
  16. 2021X2CT-FLOW: Maximum a posteriori reconstruction using a progressive flow-based deep generative model for ultra sparse-view computed tomography in ultra low-dose protocolscited by 1
  17. 2022Differentiable Uncalibrated Imagingcited by 1
  18. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  19. 2024Deep priors for satellite image restoration with accurate uncertaintiescited by 1
  20. 2022Joint Manifold Learning and Density Estimation Using Normalizing Flowscited by 0
  21. 2022Deep Invertible Approximation of Topologically Rich Maps between Manifoldscited by 0
  22. 2023Out-of-distribution detection using normalizing flows on the data manifoldcited by 0
  23. 2024Injectivity of ReLU-layers: Tools from Frame Theorycited by 0
  24. 2024Identifiable Latent Bandits: Leveraging observational data for personalized decision-makingcited by 0