A Statistical Benchmark for Diffusion Posterior Sampling Algorithms

Abstract: 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.