# Neural Variational Gradient Descent

arXiv: https://arxiv.org/abs/2107.10731 · HTML: https://mlsanity.com/paper/2107.10731/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 22 Jul 2021.

## Builds on (most cited first, 28 of 28)

- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [Function Space Particle Optimization for Bayesian Neural Networks](https://mlsanity.com/paper/1902.09754/) (2019)
- [Projected Stein Variational Gradient Descent](https://mlsanity.com/paper/2002.03469/) (2020)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [Exact Langevin Dynamics with Stochastic Gradients](https://mlsanity.com/paper/2102.01691/) (2021)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Sliced Kernelized Stein Discrepancy](https://mlsanity.com/paper/2006.16531/) (2020)
- [On Stein Variational Neural Network Ensembles](https://mlsanity.com/paper/2106.10760/) (2021)
- [BNNpriors: A library for Bayesian neural network inference with different prior distributions](https://mlsanity.com/paper/2105.06964/) (2021)
- [Stein Neural Sampler](https://mlsanity.com/paper/1810.03545/) (2018)
- [Stochastic Gradient MCMC with Repulsive Forces](https://mlsanity.com/paper/1812.00071/) (2018)
- [Operator Variational Inference](https://mlsanity.com/paper/1610.09033/) (2016)
- [Stein Self-Repulsive Dynamics: Benefits From Past Samples](https://mlsanity.com/paper/2002.09070/) (2020)
- [Kernel Stein Generative Modeling](https://mlsanity.com/paper/2007.03074/) (2020)
- [Applying SVGD to Bayesian Neural Networks for Cyclical Time-Series Prediction and Inference](https://mlsanity.com/paper/1901.05906/) (2019)

## Built on by (most cited first, 19 of 19)

- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Generative Sliced MMD Flows with Riesz Kernels](https://mlsanity.com/paper/2305.11463/) (2023)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Particle-based Variational Inference with Preconditioned Functional Gradient Flow](https://mlsanity.com/paper/2211.13954/) (2022)
- [Self-Consistent Velocity Matching of Probability Flows](https://mlsanity.com/paper/2301.13737/) (2023)
- [Entropy-based Training Methods for Scalable Neural Implicit Sampler](https://mlsanity.com/paper/2306.04952/) (2023)
- [Particle-based Variational Inference with Generalized Wasserstein Gradient Flow](https://mlsanity.com/paper/2310.16516/) (2023)
- [Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization](https://mlsanity.com/paper/2205.13098/) (2022)
- [Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels](https://mlsanity.com/paper/2301.11624/) (2023)
- [Are you using test log-likelihood correctly?](https://mlsanity.com/paper/2212.00219/) (2022)
- [Path-Guided Particle-based Sampling](https://mlsanity.com/paper/2412.03312/) (2024)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Bayesian Deep Learning for Remaining Useful Life Estimation via Stein Variational Gradient Descent](https://mlsanity.com/paper/2402.01098/) (2024)
- [Semi-Implicit Functional Gradient Flow for Efficient Sampling](https://mlsanity.com/paper/2410.17935/) (2024)
- [Accelerating Convergence of Stein Variational Gradient Descent via Deep Unfolding](https://mlsanity.com/paper/2402.15125/) (2024)
- [Functional Gradient Flows for Constrained Sampling](https://mlsanity.com/paper/2410.23170/) (2024)
- [Denoising Fisher Training For Neural Implicit Samplers](https://mlsanity.com/paper/2411.01453/) (2024)
- [Adaptive Kernel Selection for Stein Variational Gradient Descent](https://mlsanity.com/paper/2510.02067/) (2025)

## Abstract (arXiv)

Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In practice, SVGD relies on the choice of an appropriate kernel function, which impacts its ability to model the target distribution -- a challenging problem with only heuristic solutions. We propose Neural Variational Gradient Descent (NVGD), which is based on parameterizing the witness function of the Stein discrepancy by a deep neural network whose parameters are learned in parallel to the inference, mitigating the necessity to make any kernel choices whatsoever. We empirically evaluate our method on popular synthetic inference problems, real-world Bayesian linear regression, and Bayesian neural network inference.