# Generalized Doubly Reparameterized Gradient Estimators

arXiv: https://arxiv.org/abs/2101.11046 · HTML: https://mlsanity.com/paper/2101.11046/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 26 Jan 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)
- [Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization](https://mlsanity.com/paper/2006.10343/) (2020)
- [Reducing Reparameterization Gradient Variance](https://mlsanity.com/paper/1705.07880/) (2017)
- [Approximation Based Variance Reduction for Reparameterization Gradients](https://mlsanity.com/paper/2007.14634/) (2020)
- [Overdispersed Black-Box Variational Inference](https://mlsanity.com/paper/1603.01140/) (2016)

## Built on by (most cited first, 14 of 14)

- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Path-Gradient Estimators for Continuous Normalizing Flows](https://mlsanity.com/paper/2206.09016/) (2022)
- [Bridging the Gap Between Variational Inference and Wasserstein Gradient Flows](https://mlsanity.com/paper/2310.20090/) (2023)
- [Multi-Sample Training for Neural Image Compression](https://mlsanity.com/paper/2209.13834/) (2022)
- [Understanding What Affects the Generalization Gap in Visual Reinforcement Learning: Theory and Empirical Evidence](https://mlsanity.com/paper/2402.02701/) (2024)
- [Fast and Unified Path Gradient Estimators for Normalizing Flows](https://mlsanity.com/paper/2403.15881/) (2024)
- [Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VI](https://mlsanity.com/paper/2412.08824/) (2024)
- [U-Statistics for Importance-Weighted Variational Inference](https://mlsanity.com/paper/2302.13918/) (2023)
- [Path Gradients after Flow Matching](https://mlsanity.com/paper/2505.10139/) (2025)
- [VISA: Variational Inference with Sequential Sample-Average Approximations](https://mlsanity.com/paper/2403.09429/) (2024)
- [Understanding and mitigating difficulties in posterior predictive evaluation](https://mlsanity.com/paper/2405.19747/) (2024)
- [Rao-Blackwellised Reparameterisation Gradients](https://mlsanity.com/paper/2506.07687/) (2025)

## Abstract (arXiv)

Efficient low-variance gradient estimation enabled by the reparameterization trick (RT) has been essential to the success of variational autoencoders. Doubly-reparameterized gradients (DReGs) improve on the RT for multi-sample variational bounds by applying reparameterization a second time for an additional reduction in variance. Here, we develop two generalizations of the DReGs estimator and show that they can be used to train conditional and hierarchical VAEs on image modelling tasks more effectively. First, we extend the estimator to hierarchical models with several stochastic layers by showing how to treat additional score function terms due to the hierarchical variational posterior. We then generalize DReGs to score functions of arbitrary distributions instead of just those of the sampling distribution, which makes the estimator applicable to the parameters of the prior in addition to those of the posterior.