# A piecewise deterministic Monte Carlo method for diffusion bridges

arXiv: https://arxiv.org/abs/2001.05889 · HTML: https://mlsanity.com/paper/2001.05889/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2020.

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

- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Control Consistency Losses for Diffusion Bridges](https://mlsanity.com/paper/2512.05070/) (2025)
- [Score matching for sub-Riemannian bridge sampling](https://mlsanity.com/paper/2404.15258/) (2024)
- [Neural Guided Diffusion Bridges](https://mlsanity.com/paper/2502.11909/) (2025)
- [A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces](https://mlsanity.com/paper/2206.04552/) (2022)

## Abstract (arXiv)

We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the L'evy-Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber-Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local Algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.