# Implicit Variational Rejection Sampling

arXiv: https://arxiv.org/abs/2606.14235 · HTML: https://mlsanity.com/paper/2606.14235/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 66 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 30 of 49)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscaling](https://mlsanity.com/paper/1812.01608/) (2018)
- [Resampled Priors for Variational Autoencoders](https://mlsanity.com/paper/1810.11428/) (2018)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Consistency Regularization for Variational Auto-Encoders](https://mlsanity.com/paper/2105.14859/) (2021)
- [Discriminator Rejection Sampling](https://mlsanity.com/paper/1810.06758/) (2018)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Variational Inference using Implicit Distributions](https://mlsanity.com/paper/1702.08235/) (2017)
- [Unbiased Implicit Variational Inference](https://mlsanity.com/paper/1808.02078/) (2018)
- [DVAE++: Discrete Variational Autoencoders with Overlapping Transformations](https://mlsanity.com/paper/1802.04920/) (2018)
- [MaCow: Masked Convolutional Generative Flow](https://mlsanity.com/paper/1902.04208/) (2019)
- [Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms](https://mlsanity.com/paper/1610.05683/) (2016)
- [Locally Masked Convolution for Autoregressive Models](https://mlsanity.com/paper/2006.12486/) (2020)
- [Doubly Semi-Implicit Variational Inference](https://mlsanity.com/paper/1810.02789/) (2018)
- [Semi-Implicit Variational Inference via Score Matching](https://mlsanity.com/paper/2308.10014/) (2023)
- [Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference](https://mlsanity.com/paper/2407.17033/) (2024)
- [PixelVAE++: Improved PixelVAE with Discrete Prior](https://mlsanity.com/paper/1908.09948/) (2019)

## Abstract (arXiv)

Variational Inference (VI) is a fundamental inference technique in Bayesian machine learning for approximating complex posterior distributions. Traditional VI often relies on the mean-field factorization, which can inadequately capture true posterior complexity. Recent advancements have leveraged neural networks to model implicit distributions, offering increased flexibility. However, the practical constraints of neural network architectures still produces inaccuracies. In this paper, we propose a method called Implicit Variational Rejection Sampling (IVRS), which integrates implicit distributions with rejection sampling to improve the posterior approximation. Our method uses neural networks to construct implicit proposal distributions, and rejection sampling with a discriminator network that estimates the density ratio between the implicit proposal and the true posterior for refining the approximation. Towards this end, we introduce the Implicit Resampling Evidence Lower Bound (IR-ELBO) as a metric to characterize the resampled distribution's quality and derive a tighter variational lower bound. Experimental results demonstrate that our method outperforms traditional variational inference techniques.