# Structured Voronoi Sampling

arXiv: https://arxiv.org/abs/2306.03061 · HTML: https://mlsanity.com/paper/2306.03061/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [Self-Diagnosis and Self-Debiasing: A Proposal for Reducing Corpus-Based Bias in NLP](https://mlsanity.com/paper/2103.00453/) (2021)
- [Understanding Factuality in Abstractive Summarization with FRANK: A Benchmark for Factuality Metrics](https://mlsanity.com/paper/2104.13346/) (2021)
- [The E2E Dataset: New Challenges For End-to-End Generation](https://mlsanity.com/paper/1706.09254/) (2017)
- [Societal Biases in Language Generation: Progress and Challenges](https://mlsanity.com/paper/2105.04054/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Learning to Write with Cooperative Discriminators](https://mlsanity.com/paper/1805.06087/) (2018)
- [Locally Typical Sampling](https://mlsanity.com/paper/2202.00666/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [Controlled Text Generation as Continuous Optimization with Multiple Constraints](https://mlsanity.com/paper/2108.01850/) (2021)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [A Measure-Theoretic Characterization of Tight Language Models](https://mlsanity.com/paper/2212.10502/) (2022)
- [Towards Decoding as Continuous Optimization in Neural Machine Translation](https://mlsanity.com/paper/1701.02854/) (2017)
- [Enhanced gradient-based MCMC in discrete spaces](https://mlsanity.com/paper/2208.00040/) (2022)
- [Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials](https://mlsanity.com/paper/2101.11018/) (2021)

## Built on by (most cited first, 4 of 4)

- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [Self-Steering Language Models](https://mlsanity.com/paper/2504.07081/) (2025)
- [Constrained Adaptive Rejection Sampling](https://mlsanity.com/paper/2510.01902/) (2025)

## Abstract (arXiv)

Gradient-based sampling algorithms have demonstrated their effectiveness in text generation, especially in the context of controlled text generation. However, there exists a lack of theoretically grounded and principled approaches for this task. In this paper, we take an important step toward building a principled approach for sampling from language models with gradient-based methods. We use discrete distributions given by language models to define densities and develop an algorithm based on Hamiltonian Monte Carlo to sample from them. We name our gradient-based technique Structured Voronoi Sampling (SVS). In an experimental setup where the reference distribution is known, we show that the empirical distribution of SVS samples is closer to the reference distribution compared to alternative sampling schemes. Furthermore, in a controlled generation task, SVS is able to generate fluent and diverse samples while following the control targets significantly better than other methods.