# A variational approach to path estimation and parameter inference of hidden diffusion processes

arXiv: https://arxiv.org/abs/1508.00506 · HTML: https://mlsanity.com/paper/1508.00506/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2015.

## Built on by (most cited first, 10 of 10)

- [Large-Scale Wasserstein Gradient Flows](https://mlsanity.com/paper/2106.00736/) (2021)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Moment-Based Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/2103.00988/) (2021)
- [Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations](https://mlsanity.com/paper/2205.15368/) (2022)
- [Nonparametric learning of stochastic differential equations from sparse and noisy data](https://mlsanity.com/paper/2508.11597/) (2025)
- [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)
- [Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows](https://mlsanity.com/paper/2605.05606/) (2026)
- [Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals](https://mlsanity.com/paper/2610.04390/) (2026)

## Abstract (arXiv)

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing densities of the signal process. The paper then demonstrates how an efficient inference scheme, based on this variational approach to the approximation of the hidden states, can be designed to estimate the unknown parameters of stochastic differential equations. Two examples at the end illustrate the efficacy and the accuracy of the presented method.