ICML 2025

Neural Guided Diffusion Bridges
Gefan Yang 1 Frank van der Meulen 2 Stefan Sommer 1
Abstract
We propose a novel method for simulating condi-
tioned 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 meth-
ods, it offers greater robustness across various
diffusion specifications and conditioning scenar-
ios. 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, par-
tially specified by a neural network, for approxi-
mating the diffusion bridge path measure. Once
trained, it enables efficient sampling of indepen-
dent bridges at a cost comparable to sampling the
unconditioned (forward) process.
1. Introduction
Diffusion processes play a fundamental role in various fields
such as mathematics, physics, evolutionary biology, and, re-
cently, generative models. In particular, diffusion processes
conditioned to hit a specific point at a fixed future time,
which are often referred to as diffusion bridges, are of great
interest in situations where observations constrain the dy-
namics of a stochastic process. For example, in generative
modeling, stochastic imputation between two given images,
also known as the image translation task, uses diffusion
bridges to model dynamics (Zhou et al., 2024; Zheng et al.,
2025). In the area of stochastic shape analysis and computa-
tional anatomy, random evolutions of biological shapes of
organisms are modeled as non-linear diffusion bridges, and
simulating such bridges is critical to solving inference and
1Department of Computer Science, University of Copenhagen,
Universitetsparken 1, 2100 København, Denmark 2Department of
Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111,
1081HV Amsterdam...