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 reverse-process 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 propose a flexible variational family for approximating the diffusion bridge path measure which is partially specified by a neural network. Once trained, it enables efficient independent sampling at a cost comparable to sampling the unconditioned (forward) process.

We introduce a new way to simulate how random systems evolve over time when they are required to reach a specific outcome. This approach uses a neural network to learn these patterns, allowing us to avoid older, slower methods that require a lot of computer power. Our method works well even in difficult situations—like when rare events happen or when there are many possible outcomes—and it remains efficient and reliable. Once trained, it can quickly generate realistic simulations without much extra cost.