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On Diffusion Posterior Sampling: Bias and Stability

Matías G. Delgadino, Assistant Professor, Department of Mathematics at The University of Texas at Austin

Abstract

Diffusion-based posterior samplers draw from measurement- or reward-conditioned posteriors using pre trained diffusion priors. Though widely used for inverse problems, their output is biased even with exact prior scores in the Gaussian case. First, we quantify this bias for the DPS algorithm, the base method for a family of samplers, by introducing a surrogate curve of probability densities which interpolates between the true posterior and the standard Gaussian; identifying which posterior regions are over- or under-sampled. Second, we show how the original reward guidance implementation of DPS inevitably violates the forward-Euler stability criterion near the constraint.

Biography

Matías G. Delgadino is an Assistant Professor in the Department of Mathematics at The University of Texas at Austin. He received his Ph.D. from the University of Maryland, College Park in 2016, and held positions at ICTP (Trieste), Imperial College London, PUC-Rio, and the University of Oxford, before joining UT Austin in 2021. His research is in nonlinear partial differential equations and kinetic theory, with a focus on mean-field limits of interacting particle systems, optimal transport and gradient flows, and the mathematical foundations of generative modeling and sampling.