Title: A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
Primary area: datasets and benchmarks
Keywords: Diffusion models, Bayesian inverse problems, statistical evaluation, Gibbs sampling

Abstract: We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms in linear inverse problems. Our test signals are discretized Lévy processes whose posteriors admit efficient Gibbs methods. These Gibbs methods provide gold-standard posterior samples for direct, distribution-level comparisons with (DPS) algorithms. They also serve as oracle denoisers in the reverse diffusion, which enables the isolation of 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 evaluate popular algorithms on the inverse problems of denoising, deconvolution, imputation, and reconstruction from partial Fourier measurements. We release the benchmark code at https://github.com/emblem-saying/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 the community to contribute and report results.

TL;DR: We made an evaluation pipeline for diffusion posterior sampling algorithms for Bayesian linear inverse problems that relies on the construction of posteriors with known posteriors that we can efficiently sample from.