Test-Time Anchoring for Discrete Diffusion Posterior Sampling

• URL: http://arxiv.org/abs/2510.02291v1
• Date: Thu, 02 Oct 2025 17:58:37 GMT
• Title: Test-Time Anchoring for Discrete Diffusion Posterior Sampling
• Authors: Litu Rout, Andreas Lugmayr, Yasamin Jafarian, Srivatsan Varadharajan, Constantine Caramanis, Sanjay Shakkottai, Ira Kemelmacher-Shlizerman,
• Abstract summary: Posterior sampling is a challenging problem for pretrained discrete diffusion foundation models.<n>We introduce Anchored Posterior Sampling (APS) for masked diffusion foundation models.<n>Our approach achieves state-of-the-art performance among discrete diffusion samplers across linear and nonlinear inverse problems.
• Score: 38.507644561076894
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the problem of posterior sampling using pretrained discrete diffusion foundation models, aiming to recover images from noisy measurements without retraining task-specific models. While diffusion models have achieved remarkable success in generative modeling, most advances rely on continuous Gaussian diffusion. In contrast, discrete diffusion offers a unified framework for jointly modeling categorical data such as text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free Bayesian inference, making it particularly well-suited for posterior sampling. However, existing approaches to discrete diffusion posterior sampling 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) for masked diffusion foundation models, built on two key innovations -- quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. Our approach achieves state-of-the-art performance among discrete diffusion samplers across linear and nonlinear inverse problems on the standard benchmarks. We further demonstrate the benefits of our approach in training-free stylization and text-guided editing.

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