Jiequn Han (Flatiron Institute)
Provable Posterior Sampling with Denoising Oracles via Tilted Transport
Fri October 30th, 2026 - 1:00 pm6618 Morgridge HallCS Theory SeminarAbstract
Score-based diffusion models learn a denoising oracle from data and have become a standard way to represent high-dimensional data priors. From a Bayesian perspective, they should also facilitate sampling from related distributions, such as posterior distributions in inverse problems or tilted distributions shaped by additional criteria. Many heuristic methods exist for this, but most lack quantitative guarantees.
This talk focuses on the setting of linear inverse problems with Gaussian observation noise. I will introduce tilted transport, a technique grounded in the analysis of the SDEs underlying diffusion. The denoising oracle enables an exact transformation of the original posterior sampling problem into a boosted posterior that is provably easier to sample. I will quantify when the boosted posterior is strongly log-concave, with explicit dependence on the condition number of the measurement matrix and the signal-to-noise ratio, delineating a regime where sampling is provably tractable given oracle access. Recent work has shown that sampling from negative-definite quadratic tilts is intractable in general, even at rank one, indicating that some such restriction is necessary.
Joint work with Joan Bruna (arXiv:2407.00745).
