# RetroBridge: Modeling Retrosynthesis with Markov Bridges

arXiv: https://arxiv.org/abs/2308.16212 · HTML: https://mlsanity.com/paper/2308.16212/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 66 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Molecular Transformer - A Model for Uncertainty-Calibrated Chemical Reaction Prediction](https://mlsanity.com/paper/1811.02633/) (2018)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Learning to Plan Chemical Syntheses](https://mlsanity.com/paper/1708.04202/) (2017)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Retrosynthesis Prediction with Conditional Graph Logic Network](https://mlsanity.com/paper/2001.01408/) (2020)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [Molecule Edit Graph Attention Network: Modeling Chemical Reactions as Sequences of Graph Edits](https://mlsanity.com/paper/2006.15426/) (2020)
- [Retrosynthetic reaction prediction using neural sequence-to-sequence models](https://mlsanity.com/paper/1706.01643/) (2017)
- [A Graph to Graphs Framework for Retrosynthesis Prediction](https://mlsanity.com/paper/2003.12725/) (2020)

## Built on by (most cited first, 30 of 36)

- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Cometh: A continuous-time discrete-state graph diffusion model](https://mlsanity.com/paper/2406.06449/) (2024)
- [Re-evaluating Retrosynthesis Algorithms with Syntheseus](https://mlsanity.com/paper/2310.19796/) (2023)
- [Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformation](https://mlsanity.com/paper/2410.01500/) (2024)
- [MADGEN: Mass-Spec attends to De Novo Molecular generation](https://mlsanity.com/paper/2501.01950/) (2025)
- [Multi-domain Distribution Learning for De Novo Drug Design](https://mlsanity.com/paper/2508.17815/) (2025)
- [Electron flow matching for generative reaction mechanism prediction obeying conservation laws](https://mlsanity.com/paper/2502.12979/) (2025)
- [LLM-Augmented Chemical Synthesis and Design Decision Programs](https://mlsanity.com/paper/2505.07027/) (2025)
- [RetroGFN: Diverse and Feasible Retrosynthesis using GFlowNets](https://mlsanity.com/paper/2406.18739/) (2024)
- [Diffusion & Adversarial Schr"odinger Bridges via Iterative Proportional Markovian Fitting](https://mlsanity.com/paper/2410.02601/) (2024)
- [Bridge-IF: Learning Inverse Protein Folding with Markov Bridges](https://mlsanity.com/paper/2411.02120/) (2024)
- [MS-BART: Unified Modeling of Mass Spectra and Molecules for Structure Elucidation](https://mlsanity.com/paper/2510.20615/) (2025)
- [Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models](https://mlsanity.com/paper/2405.17656/) (2024)
- [RetroDiff: Retrosynthesis as Multi-stage Distribution Interpolation](https://mlsanity.com/paper/2311.14077/) (2023)
- [Chemist-aligned retrosynthesis by ensembling diverse inductive bias models](https://mlsanity.com/paper/2412.05269/) (2024)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [UAlign: Pushing the Limit of Template-free Retrosynthesis Prediction with Unsupervised SMILES Alignment](https://mlsanity.com/paper/2404.00044/) (2024)
- [Preference Optimization for Molecule Synthesis with Conditional Residual Energy-based Models](https://mlsanity.com/paper/2406.02066/) (2024)
- [Atom-anchored LLMs speak Chemistry: A Retrosynthesis Demonstration](https://mlsanity.com/paper/2510.16590/) (2025)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Order Matters in Retrosynthesis: Structure-aware Generation via Reaction-Center-Guided Discrete Flow Matching](https://mlsanity.com/paper/2602.13136/) (2026)
- [FlowMS: Flow Matching for De Novo Structure Elucidation from Mass Spectra](https://mlsanity.com/paper/2603.18397/) (2026)
- [Probabilistic Graph Circuits: Deep Generative Models for Tractable Probabilistic Inference over Graphs](https://mlsanity.com/paper/2503.12162/) (2025)
- [EnerBridge-DPO: Energy-Guided Protein Inverse Folding with Markov Bridges and Direct Preference Optimization](https://mlsanity.com/paper/2506.09496/) (2025)
- [Discrete Bridges for Mutual Information Estimation](https://mlsanity.com/paper/2602.08894/) (2026)
- [Mechanistic Reaction Prediction via Discrete Flow Matching on Graph-Structured Electron Occupation](https://mlsanity.com/paper/2608.27429/) (2026)
- [SynBridge: Bridging Reaction States via Discrete Flow for Bidirectional Reaction Prediction](https://mlsanity.com/paper/2507.08475/) (2025)

## Abstract (arXiv)

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.