Neural Guided Diffusion Bridges

TL;DR

This paper introduces a neural network-based method for efficiently simulating conditioned diffusion processes, improving robustness and computational efficiency over traditional MCMC and score-based methods, especially for complex distributions.

Contribution

It presents a novel neural-guided approach that approximates diffusion bridges without relying on MCMC or score models, enabling faster and more robust sampling.

Findings

Outperforms existing methods in robustness across various scenarios.

Enables efficient independent sampling of diffusion bridges.

Reduces computational cost to that of unconditioned process sampling.

Abstract

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive Markov Chain Monte Carlo (MCMC) methods or score modeling. Compared to existing methods, it offers greater robustness across various diffusion specifications and conditioning scenarios. This applies in particular to rare events and multimodal distributions, which pose challenges for score-learning- and MCMC-based approaches. We introduce a flexible variational family, partially specified by a neural network, for approximating the diffusion bridge path measure. Once trained, it enables efficient sampling of independent bridges at a cost comparable to sampling the unconditioned (forward) process.