We introduce Anchored Posterior Sampling (APS) for masked diffusion foundation models, built on two key innovations:

1. Quantized expectation — provides gradient-like guidance for discrete diffusion with a purely discrete embedding space.
2. Anchored remasking — enables adaptive decoding by preserving “anchor tokens” aligned with measurements.

APS supports a variety of linear and nonlinear inverse problems (super-resolution, deblurring, inpainting, HDR, nonlinear blur) as well as reference-guided stylization and text-guided editing.

APS achieves state-of-the-art performance among discrete samplers and remains competitive with continuous diffusion, while being more efficient at test time.

• [2025.10.02] Our paper is now on ArXiv!

APS produces sharper textures and refined details compared to G2D2 and DPS.

APS generalizes to multiple tasks (motion blur, HDR, nonlinear blur) with large improvements in PSNR and LPIPS.

APS enables training-free stylization with a reference style image and prompt.

APS also supports text-guided block inpainting:

APS demonstrates better scaling than continuous diffusion samplers at high resolutions, achieving strong performance with only 15 steps at 1024×1024.

If you find this work useful, please cite:

@article{rout2025aps,
  title     = {Test-Time Anchoring for Discrete Diffusion Posterior Sampling},
  author    = {Rout, L. and Lugmayr, A. and Jafarian, Y. and Varadharajn, S. and Caramanis, C. and Shakkottai, S. and Shlizerman, I.},
  journal   = {arXiv preprint arXiv:2510.02291},
  year      = {2025},
  url       = {https://arxiv.org/abs/2510.02291}     
}