# Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives

arXiv: https://arxiv.org/abs/1810.04152 · HTML: https://mlsanity.com/paper/1810.04152/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2018.

## Built on by (most cited first, 30 of 41)

- [Variational Mixture-of-Experts Autoencoders for Multi-Modal Deep Generative Models](https://mlsanity.com/paper/1911.03393/) (2019)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [MCMC Variational Inference via Uncorrected Hamiltonian Annealing](https://mlsanity.com/paper/2107.04150/) (2021)
- [On the Limitations of Multimodal VAEs](https://mlsanity.com/paper/2110.04121/) (2021)
- [Mitigating Modality Collapse in Multimodal VAEs via Impartial Optimization](https://mlsanity.com/paper/2206.04496/) (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)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Alpha-divergence Variational Inference Meets Importance Weighted Auto-Encoders: Methodology and Asymptotics](https://mlsanity.com/paper/2210.06226/) (2022)
- [Generalized Doubly Reparameterized Gradient Estimators](https://mlsanity.com/paper/2101.11046/) (2021)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Path-Gradient Estimators for Continuous Normalizing Flows](https://mlsanity.com/paper/2206.09016/) (2022)
- [Empirical Evaluation of Biased Methods for Alpha Divergence Minimization](https://mlsanity.com/paper/2105.06587/) (2021)
- [Recursive Monte Carlo and Variational Inference with Auxiliary Variables](https://mlsanity.com/paper/2203.02836/) (2022)
- [Bridging the Gap Between Variational Inference and Wasserstein Gradient Flows](https://mlsanity.com/paper/2310.20090/) (2023)
- [Innovations Autoencoder and its Application in One-class Anomalous Sequence Detection](https://mlsanity.com/paper/2106.12382/) (2021)
- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Variational Sparse Coding with Learned Thresholding](https://mlsanity.com/paper/2205.03665/) (2022)
- [Multi-Sample Training for Neural Image Compression](https://mlsanity.com/paper/2209.13834/) (2022)
- [Online Variational Sequential Monte Carlo](https://mlsanity.com/paper/2312.12616/) (2023)
- [Fast and Unified Path Gradient Estimators for Normalizing Flows](https://mlsanity.com/paper/2403.15881/) (2024)
- [Variational Inference with Holder Bounds](https://mlsanity.com/paper/2111.02947/) (2021)
- [Uphill Roads to Variational Tightness: Monotonicity and Monte Carlo Objectives](https://mlsanity.com/paper/2201.10989/) (2022)
- [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)
- [Reconstruction of Incomplete Wildfire Data using Deep Generative Models](https://mlsanity.com/paper/2201.06153/) (2022)
- [Unscented Autoencoder](https://mlsanity.com/paper/2306.05256/) (2023)
- [Reparameterized Variational Rejection Sampling](https://mlsanity.com/paper/2309.14612/) (2023)
- [Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Families](https://mlsanity.com/paper/2403.03069/) (2024)
- [Explainability as statistical inference](https://mlsanity.com/paper/2212.03131/) (2022)
- [VISA: Variational Inference with Sequential Sample-Average Approximations](https://mlsanity.com/paper/2403.09429/) (2024)

## Abstract (arXiv)

Deep latent variable models have become a popular model choice due to the scalable learning algorithms introduced by (Kingma & Welling, 2013; Rezende et al., 2014). These approaches maximize a variational lower bound on the intractable log likelihood of the observed data. Burda et al. (2015) introduced a multi-sample variational bound, IWAE, that is at least as tight as the standard variational lower bound and becomes increasingly tight as the number of samples increases. Counterintuitively, the typical inference network gradient estimator for the IWAE bound performs poorly as the number of samples increases (Rainforth et al., 2018; Le et al., 2018). Roeder et al. (2017) propose an improved gradient estimator, however, are unable to show it is unbiased. We show that it is in fact biased and that the bias can be estimated efficiently with a second application of the reparameterization trick. The doubly reparameterized gradient (DReG) estimator does not suffer as the number of samples increases, resolving the previously raised issues. The same idea can be used to improve many recently introduced training techniques for latent variable models. In particular, we show that this estimator reduces the variance of the IWAE gradient, the reweighted wake-sleep update (RWS) (Bornschein & Bengio, 2014), and the jackknife variational inference (JVI) gradient (Nowozin, 2018). Finally, we show that this computationally efficient, unbiased drop-in gradient estimator translates to improved performance for all three objectives on several modeling tasks.