# GradInf: Gradient Estimation as Probabilistic Inference

arXiv: https://arxiv.org/abs/2607.07840 · HTML: https://mlsanity.com/paper/2607.07840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 87 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 30 of 39)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [DisARM: An Antithetic Gradient Estimator for Binary Latent Variables](https://mlsanity.com/paper/2006.10680/) (2020)
- [Differentiable Rendering of Neural SDFs through Reparameterization](https://mlsanity.com/paper/2206.05344/) (2022)
- [Rao-Blackwellized Stochastic Gradients for Discrete Distributions](https://mlsanity.com/paper/1810.04777/) (2018)
- [On Correctness of Automatic Differentiation for Non-Differentiable Functions](https://mlsanity.com/paper/2006.06903/) (2020)
- [SPPL: Probabilistic Programming with Fast Exact Symbolic Inference](https://mlsanity.com/paper/2010.03485/) (2020)
- [A Convenient Category for Higher-Order Probability Theory](https://mlsanity.com/paper/1701.02547/) (2017)
- [Credit Assignment Techniques in Stochastic Computation Graphs](https://mlsanity.com/paper/1901.01761/) (2019)
- [Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing](https://mlsanity.com/paper/2001.02209/) (2020)
- [ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs](https://mlsanity.com/paper/2212.06386/) (2022)
- [Storchastic: A Framework for General Stochastic Automatic Differentiation](https://mlsanity.com/paper/2104.00428/) (2021)
- [Denotational validation of higher-order Bayesian inference](https://mlsanity.com/paper/1711.03219/) (2017)
- [Maximal couplings of the Metropolis-Hastings algorithm](https://mlsanity.com/paper/2010.08573/) (2020)
- [Gradient Estimation for Binary Latent Variables via Gradient Variance Clipping](https://mlsanity.com/paper/2208.06124/) (2022)
- [Smoothness Analysis for Probabilistic Programs with Application to Optimised Variational Inference](https://mlsanity.com/paper/2208.10530/) (2022)
- [On the Versatility of Open Logical Relations: Continuity, Automatic Differentiation, and a Containment Theorem](https://mlsanity.com/paper/2002.08489/) (2020)
- [Conditional independence by typing](https://mlsanity.com/paper/2010.11887/) (2020)
- [Probabilistic Programming with Programmable Variational Inference](https://mlsanity.com/paper/2406.15742/) (2024)
- [A Separation Logic for Concurrent Randomized Programs](https://mlsanity.com/paper/1802.02951/) (2018)

## Abstract (arXiv)

Gradient estimation -- the task of computing the gradient of the expected value of a probabilistic program -- has diverse applications in scientific computing, but is notoriously difficult because of issues such as high-dimensional integration, discrete random choices, and complex stochastic dependencies. This article introduces gradient inference, a new approach to developing sound and efficient gradient estimators for probabilistic programs. Gradient inference rests on a formal reduction from a gradient estimation problem to a closely related probabilistic inference problem, whose solution can be differentiated to obtain a gradient estimator. This inference problem is obtained by applying two powerful statistical operations -- coupling and factorization -- to the input probabilistic program. Our reduction lets us leverage the rich toolkit of probabilistic inference algorithms to design novel gradient estimators that extend and improve upon existing methods. We introduce GradInf, a probabilistic programming system that facilitates the sound and automated implementation of gradient inference. GradInf is centered around programmable source-to-source transformations for coupling and factorizing higher-order probabilistic programs, whose soundness is proven in terms of a denotational semantics. Key to our development is the use of information-flow typing to allow random choices in a probabilistic program to be factored out and partially evaluated, which improves our ability to deploy sophisticated probabilistic inference algorithms. The resulting system offers practitioners a principled framework for designing gradient estimators. We apply GradInf to several challenging case studies, showing that it can express prominent gradient estimators from the literature and enables the construction of new state-of-the-art estimators that outperform the best existing baselines.