mlsanityData to 14 Oct 2026

Stabilizing Invertible Neural Networks Using Mixture Models

arXiv 2009.02994 ↗First posted 7 Sep 2020cs.LG math.OC stat.MLcited by 30

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Abstract (arXiv)

In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks. Without such an control, numerical simulations are prone to errors and not much is gained against traditional approaches. Fortunately, our analysis indicates that changing the latent distribution from a standard normal one to a Gaussian mixture model resolves the issue of exploding Lipschitz constants. Indeed, numerical simulations confirm that this modification leads to significantly improved sampling quality in multimodal applications.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). First posted on arXiv 7 Sep 2020.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 9; 2024: 3; 2025: 3; 2026: 2.

30 papers.

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  1. 2021An Introduction to Deep Generative Modelingcited by 104
  2. 2021Resampling Base Distributions of Normalizing Flowscited by 42
  3. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  4. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  5. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  6. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 24
  7. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  8. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  9. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  10. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 13
  11. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 13
  12. 2021Invertible Neural Networks versus MCMC for Posterior Reconstruction in Grazing Incidence X-Ray Fluorescencecited by 12
18 more
  1. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  2. 2022Stability of Image-Reconstruction Algorithmscited by 7
  3. 2023Normalizing flow sampling with Langevin dynamics in the latent spacecited by 7
  4. 2023Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learningcited by 7
  5. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  6. 2022Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spacescited by 6
  7. 2024Stable Training of Normalizing Flows for High-dimensional Variational Inferencecited by 6
  8. 2022Proximal Residual Flows for Bayesian Inverse Problemscited by 5
  9. 2024(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Numbercited by 5
  10. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  11. 2023Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problemscited by 3
  12. 2026Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Oncecited by 3
  13. 2023On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networkscited by 2
  14. 2023Piecewise Normalizing Flowscited by 1
  15. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  16. 2025Noise-adapted Neural Operator for Robust Non-Line-of-Sight Imagingcited by 1
  17. 2025Adapting Noise to Data: Generative Flows from 1D Processescited by 0
  18. 2026Simplifying Flow Matching Transformations with Low-Rank Mixture Modelscited by 0