# A Statistical Benchmark for Diffusion Posterior Sampling Algorithms

arXiv: https://arxiv.org/abs/2509.12821 · HTML: https://mlsanity.com/paper/2509.12821/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2025.

## Built on by (most cited first, 6 of 6)

- [Robust Inference-Time Steering of Protein Diffusion Models via Embedding Optimization](https://mlsanity.com/paper/2602.05285/) (2026)
- [A Stability Benchmark of Generative Regularizers for Inverse Problems](https://mlsanity.com/paper/2605.10076/) (2026)
- [A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2606.12710/) (2026)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)
- [Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers](https://mlsanity.com/paper/2602.04189/) (2026)
- [MoRF-AST: Calibrated Probabilistic Virtual Sensing for Structural Monitoring under Changing Operating Conditions](https://mlsanity.com/paper/2608.24531/) (2026)

## Abstract (arXiv)

We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse L'evy-process priors whose posteriors admit efficient Gibbs methods. These Gibbs methods can be used to obtain gold-standard posterior samples that can be compared to the samples obtained by the DPS algorithms. By using the Gibbs methods for the resolution of the denoising problems in the reverse diffusion, the framework also isolates the error that arises from the approximations to the likelihood score. We instantiate the benchmark with the minimum-mean-squared-error optimality gap and posterior coverage tests and provide numerical experiments for popular DPS algorithms on the inverse problems of denoising, deconvolution, imputation, and reconstruction from partial Fourier measurements. We release the benchmark code at https://github.com/zacmar/dps-benchmark. The repository exposes simple plug-in interfaces, reference scripts, and config-driven runs so that new algorithms can be added and evaluated with minimal effort. We invite researchers to contribute and report results.