# A variational approach to sampling in diffusion processes

arXiv: https://arxiv.org/abs/2405.00126 · HTML: https://mlsanity.com/paper/2405.00126/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [Latent Abstractions in Generative Diffusion Models](https://mlsanity.com/paper/2410.03368/) (2024)
- [Pathwise Learning of Stochastic Dynamical Systems with Partial Observations](https://mlsanity.com/paper/2601.21860/) (2026)
- [Dual Filter: A Transformer-like Inference Architecture for Hidden Markov Models](https://mlsanity.com/paper/2505.00818/) (2025)
- [Machine-Learned Sampling of Conditioned Path Measures](https://mlsanity.com/paper/2506.01904/) (2025)

## Abstract (arXiv)

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 Schr"odinger bridges.