# Your Absorbing Discrete Diffusion Secretly Models the Bayesian Posterior

arXiv: https://arxiv.org/abs/2507.07586 · HTML: https://mlsanity.com/paper/2507.07586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 7 of its 8 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 7 of 7)

- [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)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)

## Abstract (arXiv)

Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected denoiser output under the forward corruption distribution recovers the true posterior, and that a simple Monte Carlo estimator converges to this posterior at rate O(1/sqrt(K)) with finite-sample concentration bounds. Building on this insight, we introduce an inference-time ensemble that runs K independent denoising passes and aggregates both posterior means and variances without any extra training. On WikiText-2, our MC-marginal sampler recovers the analytic lambda-DCE zero-shot perplexity (approximately 39) to within a few points at K=128, and its per-token variance shows a strong rank correlation with reconstruction error (Spearman rho = 0.996). This cost-proportional procedure yields calibrated uncertainty estimates and a direct trade-off between compute and posterior fidelity in discrete diffusion LMs.