mlsanityData to 7 Oct 2026

VarGrad: A Low-Variance Gradient Estimator for Variational Inference

arXiv 2010.10436 ↗First posted 20 Oct 2020stat.ML cs.LG math.STcited by 73

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Abstract (arXiv)

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the textitlog-variance loss. Under certain conditions, the gradient of the log-variance loss equals the gradient of the (negative) ELBO. We show theoretically that this gradient estimator, which we call textitVarGrad due to its connection to the log-variance loss, exhibits lower variance than the score function method in certain settings, and that the leave-one-out control variate coefficients are close to the optimal ones. We empirically demonstrate that VarGrad offers a favourable variance versus computation trade-off compared to other state-of-the-art estimators on a discrete VAE.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Oct 2020.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 8; 2024: 15; 2025: 24; 2026: 15.

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  1. 2024Generalized Preference Optimization: A Unified Approach to Offline Alignmentcited by 155
  2. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
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  7. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
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  9. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  10. 2024Improved off-policy training of diffusion samplerscited by 47
  11. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  12. 2025Prompt Curriculum Learning for Efficient LLM Post-Trainingcited by 40
38 more
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  4. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  5. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  6. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  7. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  8. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  9. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  10. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  11. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  12. 2025Learning to Sample Effective and Diverse Prompts for Text-to-Image Generationcited by 16
  13. 2023Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trickcited by 13
  14. 2024Improved Off-policy Reinforcement Learning in Biological Sequence Designcited by 13
  15. 2024Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplerscited by 10
  16. 2021Coupled Gradient Estimators for Discrete Latent Variablescited by 9
  17. 2023Designing losses for data-free training of normalizing flows on Boltzmann distributionscited by 9
  18. 2023GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologiescited by 9
  19. 2021Double Control Variates for Gradient Estimation in Discrete Latent Variable Modelscited by 8
  20. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
  21. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
  22. 2021Leveraging Recursive Gumbel-Max Trick for Approximate Inference in Combinatorial Spacescited by 7
  23. 2025Rethinking Losses for Diffusion Bridge Samplerscited by 7
  24. 2024On Divergence Measures for Training GFlowNetscited by 6
  25. 2025Iterative Importance Fine-tuning of Diffusion Modelscited by 6
  26. 2025Adaptive Destruction Processes for Diffusion Samplerscited by 6
  27. 2023Adaptive Instrument Design for Indirect Experimentscited by 5
  28. 2024Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VIcited by 5
  29. 2025Data-to-Energy Stochastic Dynamicscited by 5
  30. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 5
  31. 2021CARMS: Categorical-Antithetic-REINFORCE Multi-Sample Gradient Estimatorcited by 4
  32. 2024Streaming Bayes GFlowNetscited by 4
  33. 2025End-To-End Learning of Gaussian Mixture Priors for Diffusion Samplercited by 4
  34. 2025A friendly introduction to triangular transportcited by 4
  35. 2024Embarrassingly Parallel GFlowNetscited by 3
  36. 2026f-Trajectory Balance: A Loss Family for Tuning GFlowNets, Generative Models, and LLMs with Off- and On-Policy Datacited by 3
  37. 2026Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inferencecited by 3
  38. 2026ReCache: Learning Budget-Aware Caching Schedules for Diffusion Models via REINFORCEcited by 3

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