# Test-Time Anchoring for Discrete Diffusion Posterior Sampling

arXiv: https://arxiv.org/abs/2510.02291 · HTML: https://mlsanity.com/paper/2510.02291/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 55 of its 77 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 55)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)

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

- [Entropy Aware Reward Guidance for Diffusion Language Model Alignment](https://mlsanity.com/paper/2602.05000/) (2026)
- [AnCoder: Anchored Code Generation via Discrete Diffusion Models](https://mlsanity.com/paper/2602.17688/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Discrete Langevin-Inspired Posterior Sampling](https://mlsanity.com/paper/2605.09302/) (2026)
- [FastGuide: Accelerating Reward Guidance for Diffusion Large Language Models](https://mlsanity.com/paper/2609.36202/) (2026)

## Abstract (arXiv)

While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free guidance, making it well-suited for posterior sampling. Existing approaches to posterior sampling using discrete diffusion face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS), built on two key innovations: quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. APS achieves state-of-the-art performance among discrete diffusion samplers on both linear and nonlinear inverse problems across the standard image benchmarks. We demonstrate the generality of APS through training-free stylization and text-guided editing. We further apply APS to a large-scale diffusion language model, showing consistent improvement in question answering.