# Optimal Budgeted Rejection Sampling for Generative Models

arXiv: https://arxiv.org/abs/2311.00460 · HTML: https://mlsanity.com/paper/2311.00460/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models](https://mlsanity.com/paper/2211.17091/) (2022)
- [Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling](https://mlsanity.com/paper/2003.06060/) (2020)
- [Discriminator Rejection Sampling](https://mlsanity.com/paper/1810.06758/) (2018)
- [Refining Deep Generative Models via Discriminator Gradient Flow](https://mlsanity.com/paper/2012.00780/) (2020)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Metropolis-Hastings Generative Adversarial Networks](https://mlsanity.com/paper/1811.11357/) (2018)
- [Discriminator optimal transport](https://mlsanity.com/paper/1910.06832/) (2019)
- [TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models](https://mlsanity.com/paper/2306.08013/) (2023)
- [Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows](https://mlsanity.com/paper/2305.18910/) (2023)
- [Latent reweighting, an almost free improvement for GANs](https://mlsanity.com/paper/2110.09803/) (2021)

## Built on by (most cited first, 5 of 5)

- [Improving Diversity in Language Models: When Temperature Fails, Change the Loss](https://mlsanity.com/paper/2508.09654/) (2025)
- [Jackpot: Optimal Budgeted Rejection Sampling for Extreme Actor-Policy Mismatch Reinforcement Learning](https://mlsanity.com/paper/2602.06107/) (2026)
- [Improving Discriminator Guidance in Diffusion Models](https://mlsanity.com/paper/2503.16117/) (2025)
- [Multimodal Diffusion to Mutually Enhance Polarized Light and Low Resolution EBSD Data](https://mlsanity.com/paper/2604.22212/) (2026)
- [Implicit Variational Rejection Sampling](https://mlsanity.com/paper/2606.14235/) (2026)

## Abstract (arXiv)

Rejection sampling methods have recently been proposed to improve the performance of discriminator-based generative models. However, these methods are only optimal under an unlimited sampling budget, and are usually applied to a generator trained independently of the rejection procedure. We first propose an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal with respect to textitany f-divergence between the true distribution and the post-rejection distribution, for a given sampling budget. Second, we propose an end-to-end method that incorporates the sampling scheme into the training procedure to further enhance the model's overall performance. Through experiments and supporting theory, we show that the proposed methods are effective in significantly improving the quality and diversity of the samples.