# Implicit Reparameterization Gradients

arXiv: https://arxiv.org/abs/1805.08498 · HTML: https://mlsanity.com/paper/1805.08498/

## Key facts

- Cited by 85 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 30 of 85)

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- [A unified view of likelihood ratio and reparameterization gradients](https://mlsanity.com/paper/2105.14900/) (2021)
- [Storchastic: A Framework for General Stochastic Automatic Differentiation](https://mlsanity.com/paper/2104.00428/) (2021)
- [Continuous normalizing flows on manifolds](https://mlsanity.com/paper/2104.14959/) (2021)
- [A Hierarchical Variational Neural Uncertainty Model for Stochastic Video Prediction](https://mlsanity.com/paper/2110.03446/) (2021)
- [A VAE Approach to Sample Multivariate Extremes](https://mlsanity.com/paper/2306.10987/) (2023)
- [Model-free Policy Learning with Reward Gradients](https://mlsanity.com/paper/2103.05147/) (2021)
- [Reinforcement Learning in Presence of Discrete Markovian Context Evolution](https://mlsanity.com/paper/2202.06557/) (2022)
- [Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms](https://mlsanity.com/paper/2310.19927/) (2023)
- [Contextual Feature Selection with Conditional Stochastic Gates](https://mlsanity.com/paper/2312.14254/) (2023)
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- [Rectified Max-Value Entropy Search for Bayesian Optimization](https://mlsanity.com/paper/2202.13597/) (2022)
- [Understanding What Affects the Generalization Gap in Visual Reinforcement Learning: Theory and Empirical Evidence](https://mlsanity.com/paper/2402.02701/) (2024)
- [Differentiable Feature Selection, a Reparameterization Approach](https://mlsanity.com/paper/2107.10030/) (2021)
- [Physics-informed Variational Autoencoders for Improved Robustness to Environmental Factors of Variation](https://mlsanity.com/paper/2210.10418/) (2022)
- [iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning](https://mlsanity.com/paper/2405.00285/) (2024)
- [Learning to Discover Regulatory Elements for Gene Expression Prediction](https://mlsanity.com/paper/2502.13991/) (2025)
- [A Deep Variational Bayesian Framework for Blind Image Deblurring](https://mlsanity.com/paper/2106.02884/) (2021)
- [Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling](https://mlsanity.com/paper/2110.06021/) (2021)
- [RepMode: Learning to Re-parameterize Diverse Experts for Subcellular Structure Prediction](https://mlsanity.com/paper/2212.10066/) (2022)
- [Differentiable Rendering with Reparameterized Volume Sampling](https://mlsanity.com/paper/2302.10970/) (2023)
- [The Lie-Group Bayesian Learning Rule](https://mlsanity.com/paper/2303.04397/) (2023)
- [How to Choose a Reinforcement-Learning Algorithm](https://mlsanity.com/paper/2407.20917/) (2024)

## Abstract (arXiv)

By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our experiments show that the proposed approach is faster and more accurate than the existing gradient estimators for these distributions.