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DOI: 10.23952/cot.2026.30
Received January 20, 2025; Accepted May 16, 2025; Published online March 18, 2026
Abstract. We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes’ formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem in stochastic optimal control, so that the posterior density of the signal given the observation path could be sampled by adding a drift to the signal process. We show that this control-theoretic approach to sampling provides a common mechanism underlying several distinct problems involving diffusion processes, specifically importance sampling using Feynman-Kac averages, time reversal, and Schrödinger bridges.
How to Cite this Article:
M. Raginsky, A variational approach to sampling in diffusion processes, Commun. Optim. Theory 2026 (2026) 30.