  Retrosynthesis planning is a fundamental challenge in chemistry which aims at
designing reaction pathways from commercially available starting materials to a
target molecule. Each step in multi-step retrosynthesis planning requires
accurate prediction of possible precursor molecules given the target molecule
and confidence estimates to guide heuristic search algorithms. We model
single-step retrosynthesis planning as a distribution learning problem in a
discrete state space. First, we introduce the Markov Bridge Model, a generative
framework aimed to approximate the dependency between two intractable discrete
distributions accessible via a finite sample of coupled data points. Our
framework is based on the concept of a Markov bridge, a Markov process pinned
at its endpoints. Unlike diffusion-based methods, our Markov Bridge Model does
not need a tractable noise distribution as a sampling proxy and directly
operates on the input product molecules as samples from the intractable prior
distribution. We then address the retrosynthesis planning problem with our
novel framework and introduce RetroBridge, a template-free retrosynthesis
modeling approach that achieves state-of-the-art results on standard evaluation
benchmarks.
