# Doubly Semi-Implicit Variational Inference

arXiv: https://arxiv.org/abs/1810.02789 · HTML: https://mlsanity.com/paper/1810.02789/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2018.

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

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- [Learning to Jump: Thinning and Thickening Latent Counts for Generative Modeling](https://mlsanity.com/paper/2305.18375/) (2023)
- [Star-Shaped Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.05259/) (2023)
- [Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superposition](https://mlsanity.com/paper/2301.08292/) (2023)
- [Kernel Semi-Implicit Variational Inference](https://mlsanity.com/paper/2405.18997/) (2024)
- [Structured Dropout Variational Inference for Bayesian Neural Networks](https://mlsanity.com/paper/2102.07927/) (2021)
- [Implicit Variational Inference for High-Dimensional Posteriors](https://mlsanity.com/paper/2310.06643/) (2023)
- [Lifelong Generative Modelling Using Dynamic Expansion Graph Model](https://mlsanity.com/paper/2112.08370/) (2021)
- [Symmetric Equilibrium Learning of VAEs](https://mlsanity.com/paper/2307.09883/) (2023)
- [Nonparametric Automatic Differentiation Variational Inference with Spline Approximation](https://mlsanity.com/paper/2403.06302/) (2024)
- [BayesCNS: A Unified Bayesian Approach to Address Cold Start and Non-Stationarity in Search Systems at Scale](https://mlsanity.com/paper/2410.02126/) (2024)
- [VFDS: Variational Foresight Dynamic Selection in Bayesian Neural Networks for Efficient Human Activity Recognition](https://mlsanity.com/paper/2204.00130/) (2022)
- [Inversion of Bayesian Networks](https://mlsanity.com/paper/2212.10649/) (2022)
- [Parameter Estimation in DAGs from Incomplete Data via Optimal Transport](https://mlsanity.com/paper/2305.15927/) (2023)
- [A Kernel Approach for Semi-implicit Variational Inference](https://mlsanity.com/paper/2601.12023/) (2026)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)
- [Revisiting Unbiased Implicit Variational Inference](https://mlsanity.com/paper/2506.03839/) (2025)
- [Variational Inference for Quantum HyperNetworks](https://mlsanity.com/paper/2506.05888/) (2025)
- [Implicit Variational Rejection Sampling](https://mlsanity.com/paper/2606.14235/) (2026)

## Abstract (arXiv)

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.