RetroBridge: Modeling Retrosynthesis with Markov Bridges

TL;DR

This work reframes retrosynthesis planning as learning the probabilistic dependency between two intractable discrete distributions: the product space $p_{mathcal{X}}$ and the reactant space $p_{mathcal{Y}}$. It introduces the Markov Bridge Model, a generative framework that uses trajectory sampling between endpoints to approximate this dependency, and applies it to chemistry through RetroBridge, a template-free single-step retrosynthesis method. Empirical results on USPTO-50k show RetroBridge achieving state-of-the-art performance among template-free approaches and competitive performance versus template-based methods, with explicit uncertainty-based scoring for sample ranking. The approach highlights the advantages of sequential, probabilistic mapping over diffusion-based methods when modeling mappings between two discrete distributions, and points to future directions in conditioning, reaction types, and multi-step planning for practical deployment.

Abstract

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.

Figures (6)

• Figure 1: Markov bridges between the distribution of products and distribution of reactants.
• Figure 2: The process of changing atom types along the trajectory of the Markov bridge. The trajectory starts at time step $t=0$ with the product molecule and several disconnected "dummy" atoms that will be included in the final reactant molecule. The probability of sampling the target atom type increases as $t$ grows. Five circles filled with different colors represent these probabilities. To make the illustration less bulky, we omitted a part of the product molecule and one of two reactant molecules.
• Figure 3: Examples of modeled reactants. We selected three random inputs from the test set and for each of them we provide the top-3 RetroBridge predictions along with their confidence scores. Two check marks indicate that sampled reactants are the same as the ground truth, and one check mark means that reactants are different, but Molecular Transformer schwaller2019molecular predicts the product molecule used as input.
• Figure 4: Architecture of the network that approximates the final state of the Markov bridge process (A) and scheme of the Graph Transformer Layer (B).
• Figure 5: (A) Dependency of the RetroBridge performance on the number of sampling steps. Experiment performed on the RetroBrdige with CE loss on the validation set with 50 samples per product. (B) Dependency of the RetroBridge performance on the number of samples. Experiment performed on the RetroBrdige with VLB loss on the test set with 500 sampling steps.