# A Kernel Approach for Semi-implicit Variational Inference

arXiv: https://arxiv.org/abs/2601.12023 · HTML: https://mlsanity.com/paper/2601.12023/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 84 references that are in the map.
- First posted on arXiv 17 Jan 2026.

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [A Spectral Approach to Gradient Estimation for Implicit Distributions](https://mlsanity.com/paper/1806.02925/) (2018)
- [Variational Inference using Implicit Distributions](https://mlsanity.com/paper/1702.08235/) (2017)
- [Accelerated Information Gradient flow](https://mlsanity.com/paper/1909.02102/) (2019)
- [Dimension-independent likelihood-informed MCMC](https://mlsanity.com/paper/1411.3688/) (2014)

## Built on by (most cited first, 1 of 1)

- [Conditional Kernel Stein Discrepancy](https://mlsanity.com/paper/2610.11863/) (2026)

## Abstract (arXiv)

Semi-implicit variational inference (SIVI) enhances the expressiveness of variational families through hierarchical semi-implicit distributions, but the intractability of their densities makes standard ELBO-based optimization biased. Recent score-matching approaches to SIVI (SIVI-SM) address this issue via a minimax formulation, at the expense of an additional lower-level optimization problem. In this paper, we propose kernel semi-implicit variational inference (KSIVI), a principled and tractable alternative that eliminates the lower-level optimization by leveraging kernel methods. We show that when optimizing over a reproducing kernel Hilbert space, the lower-level problem admits an explicit solution, reducing the objective to the kernel Stein discrepancy (KSD). Exploiting the hierarchical structure of semi-implicit distributions, the resulting KSD objective can be efficiently optimized using stochastic gradient methods. We establish optimization guarantees via variance bounds on Monte Carlo gradient estimators and derive statistical generalization bounds of order tildeO(1/√n). We further introduce a multi-layer hierarchical extension that improves expressiveness while preserving tractability. Empirical results on synthetic and real-world Bayesian inference tasks demonstrate the effectiveness of KSIVI.