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Generalized Normalizing Flows via Markov Chains

arXiv 2111.12506 ↗First posted 24 Nov 2021cs.LG math.PRcited by 23

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Abstract (arXiv)

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as a pair of Markov chains fulfilling some properties and show how many state-of-the-art models for data generation fit into this framework. Indeed numerical simulations show that including stochastic layers improves the expressivity of the network and allows for generating multimodal distributions from unimodal ones. The Markov chains point of view enables us to couple both deterministic layers as invertible neural networks and stochastic layers as Metropolis-Hasting layers, Langevin layers, variational autoencoders and diffusion normalizing flows in a mathematically sound way. Our framework establishes a useful mathematical tool to combine the various approaches.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 53 of its 92 references that are in the map. First posted on arXiv 24 Nov 2021.

Builds on

53 of 92 references.

References · 53

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38 more
  1. 2018Computational Optimal Transportcited by 780
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  3. 2021Score-based Generative Modeling in Latent Spacecited by 636
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  10. 2019Diagnosing and Enhancing VAE Modelscited by 193
  11. 2019Learning Likelihoods with Conditional Normalizing Flowscited by 172
  12. 2017Multiplicative Normalizing Flows for Variational Bayesian Neural Networkscited by 157
  13. 2020Stochastic Normalizing Flowscited by 157
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Citing papers per year: 2022: 2; 2023: 12; 2024: 6; 2025: 3.

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  1. 2024Sequential Controlled Langevin Diffusionscited by 48
  2. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 38
  3. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  4. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 37
  5. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 36
  6. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 19
  7. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 17
  8. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 13
  9. 2025Amortized Sampling with Transferable Normalizing Flowscited by 12
  10. 2022WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolutioncited by 10
  11. 2023Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernelscited by 9
  12. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
11 more
  1. 2024Importance Corrected Neural JKO Samplingcited by 7
  2. 2024S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domaincited by 6
  3. 2022Proximal Residual Flows for Bayesian Inverse Problemscited by 5
  4. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  5. 2023Refining Amortized Posterior Approximations using Gradient-Based Summary Statisticscited by 3
  6. 2023Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distancescited by 3
  7. 2023Generalised Scale-Space Properties for Probabilistic Diffusion Modelscited by 1
  8. 2023Variations and Relaxations of Normalizing Flowscited by 1
  9. 2024Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphscited by 1
  10. 2024Mixed Noise and Posterior Estimation with Conditional DeepGEMcited by 1
  11. 2023Generalised Diffusion Probabilistic Scale-Spacescited by 0