# Discrete Diffusion with Sample-Efficient Estimators for Conditionals

arXiv: https://arxiv.org/abs/2602.20293 · HTML: https://mlsanity.com/paper/2602.20293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [A Survey on Diffusion Language Models](https://mlsanity.com/paper/2508.10875/) (2025)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization](https://mlsanity.com/paper/2402.08095/) (2024)
- [Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models](https://mlsanity.com/paper/1605.07252/) (2016)
- [Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces](https://mlsanity.com/paper/2305.11089/) (2023)
- [Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis](https://mlsanity.com/paper/2410.02321/) (2024)
- [Glauber Generative Model: Discrete Diffusion Models via Binary Classification](https://mlsanity.com/paper/2405.17035/) (2024)
- [Learning of Discrete Graphical Models with Neural Networks](https://mlsanity.com/paper/2006.11937/) (2020)
- [Learning Energy-Based Representations of Quantum Many-Body States](https://mlsanity.com/paper/2304.04058/) (2023)

## Abstract (arXiv)

We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than approximating a discrete analog of a score function, our formulation treats single-site conditional probabilities as the fundamental objects that parameterize the reverse diffusion process. We employ a sample-efficient method known as Neural Interaction Screening Estimator (NeurISE) to estimate these conditionals in the diffusion dynamics. Controlled experiments on synthetic Ising models, MNIST, and scientific data sets produced by a D-Wave quantum annealer, synthetic Potts model and one dimensional quantum systems demonstrate the proposed approach. On the binary data sets, these experiments demonstrate that the proposed approach outperforms popular existing methods including ratio-based approaches, achieving improved performance in total variation, cross-correlations, and kernel density estimation metrics.