# Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

arXiv: https://arxiv.org/abs/2010.03509 · HTML: https://mlsanity.com/paper/2010.03509/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Conditioning non-linear and infinite-dimensional diffusion processes](https://mlsanity.com/paper/2402.01434/) (2024)
- [Score matching for bridges without learning time-reversals](https://mlsanity.com/paper/2407.15455/) (2024)
- [Control of Stochastic Quantum Dynamics by Differentiable Programming](https://mlsanity.com/paper/2101.01190/) (2021)
- [A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting](https://mlsanity.com/paper/2409.14585/) (2024)
- [Nonlinear filtering based on density approximation and deep BSDE prediction](https://mlsanity.com/paper/2508.10630/) (2025)

## Abstract (arXiv)

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.