mlsanityData to 14 Oct 2026

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

arXiv 2207.08219 ↗First posted 17 Jul 2022cs.LG stat.MLcited by 23

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Abstract (arXiv)

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to implement, have lower variance, and lead not only to faster convergence of training but also to better overall approximation results compared to standard total gradient estimators. We also demonstrate that path-gradient training is less susceptible to mode-collapse. In light of our results, we expect that path-gradient estimators will become the new standard method to train normalizing flows for variational inference.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 25 of its 39 references that are in the map. First posted on arXiv 17 Jul 2022.

Builds on

25 of 39 references.

References · 25

  1. 2013Auto-Encoding Variational Bayescited by 4,053
  2. 2015Importance Weighted Autoencoderscited by 456
  3. 2017Parallel WaveNet: Fast High-Fidelity Speech Synthesiscited by 215
  4. 2020Stochastic Normalizing Flowscited by 157
  5. 2018Neural Importance Samplingcited by 155
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  7. 2014Neural Variational Inference and Learning in Belief Networkscited by 117
  8. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
  9. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
  10. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 98
  11. 2020Sampling using SU(N) gauge equivariant flowscited by 84
  12. 2020VarGrad: A Low-Variance Gradient Estimator for Variational Inferencecited by 75
13 more
  1. 2014Reweighted Wake-Sleepcited by 66
  2. 2018Doubly Reparameterized Gradient Estimators for Monte Carlo Objectivescited by 41
  3. 2020Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimizationcited by 37
  4. 2018Pathwise Derivatives Beyond the Reparameterization Trickcited by 36
  5. 2021Challenges and Opportunities in High-dimensional Variational Inferencecited by 35
  6. 2021Flow-based sampling for multimodal and extended-mode distributions in lattice field theorycited by 25
  7. 2016Reparameterization Gradients through Acceptance-Rejection Sampling Algorithmscited by 22
  8. 2020On the Difficulty of Unbiased Alpha Divergence Minimizationcited by 21
  9. 2021Generalized Doubly Reparameterized Gradient Estimatorscited by 14
  10. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 11
  11. 2021Empirical Evaluation of Biased Methods for Alpha Divergence Minimizationcited by 10
  12. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  13. 2019Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Samplingcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 9; 2025: 3; 2026: 5.

23 papers.

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  1. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  2. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  3. 2023Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theoriescited by 25
  4. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  5. 2023Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probabilitycited by 11
  6. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
  7. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  8. 2024Stable Training of Normalizing Flows for High-dimensional Variational Inferencecited by 6
  9. 2024Practical applications of machine-learned flows on gauge fieldscited by 6
  10. 2025Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimationcited by 6
  11. 2024Conditional Normalizing Flows for Active Learning of Coarse-Grained Molecular Representationscited by 5
  12. 2024Fast and Unified Path Gradient Estimators for Normalizing Flowscited by 5
11 more
  1. 2026Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixturescited by 4
  2. 2025Path Gradients after Flow Matchingcited by 3
  3. 2026Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularizationcited by 3
  4. 2023Training normalizing flows with computationally intensive target probability distributionscited by 2
  5. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  6. 2024Mixed Noise and Posterior Estimation with Conditional DeepGEMcited by 1
  7. 2024Preferential Normalizing Flowscited by 1
  8. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  9. 2026Non-Stationarity Breaks Permutation Surrogates in Multi-Agent Reinforcement Learning: Diagnosis and Remediescited by 0
  10. 2026Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variationcited by 0
  11. 2026Scaling Online Optimal Transport Minibatches for Flow Matchingcited by 0