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RetroBridge: Modeling Retrosynthesis with Markov Bridges

Ilia Igashov, Arne Schneuing, Marwin Segler, Michael Bronstein, Bruno Correia

arXiv:2308.16212v2q-bio.QMcs.LGq-bio.BM

TL;DR

Retrosynthesis planning must predict precursor molecules for a target, but learning the dependency between product and reactant distributions poses a discrete modeling challenge. The paper introduces Markov Bridge Models and applies them in RetroBridge, a template-free retrosynthesis method. RetroBridge achieves state-of-the-art results on standard benchmarks, and the experiments favor this probabilistic framework over straightforward diffusion adaptations for the task.

  • Problem

    Retrosynthesis requires predicting possible precursors for target molecules, while the dependency between two intractable discrete distributions is not naturally modeled by approaches designed for one distribution.

    Source: §1 · pp. 1–2

  • Method

    The Markov Bridge Model learns dependencies between two intractable discrete distributions from finite coupled samples, and RetroBridge applies it to template-free single-step retrosynthesis.

    Source: §1 · p. 2, §3.1 · p. 3, §3.2 · p. 5

  • Results

    RetroBridge achieves state-of-the-art results on common evaluation benchmarks, and experiments show that this probabilistic framework performs better on the task than straightforward diffusion adaptations.

    Source: §1 · p. 2, §5 · p. 9

  • Takeaways & Limitations

    The framework may also be applied to other settings that map discrete distributions accessible through finite coupled samples, including image-to-image translation, text translation, and protein-binder design.

    Source: §5 · p. 9

    Like most related methods, RetroBridge does not directly predict experimental conditions, on which chemical reactions heavily depend.

    Source: §5 · p. 9

Abstract

from arXiv · show

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.

1 INTRODUCTION

Retrosynthesis can supply the synthetic pathways needed to test computationally designed molecules, but predicting those pathways is challenging. RetroBridge models retrosynthesis as learning a probabilistic dependency between product and reactant distributions, using Markov bridges, and achieves state-of-the-art results on standard benchmarks.

1 INTRODUCTION

  • Retrosynthesis planning proposes reaction steps or pathways that can be validated and optimized in the lab, addressing the challenge of testing computationally designed molecules whose synthesizability has received limited emphasis.Applying single-step predictions recursively can decompose a target into simpler intermediates and eventually available starting molecules.Source: §1 · p. 1
  • A probabilistic formulation represents the fact that one product can have different reactant and reagent sets, while supporting uncertainty modeling and diverse pathway generation.Source: §1 · p. 1
  • Diffusion models typically map simple prior noise to one complex data distribution, whereas retrosynthesis requires learning a dependency between two intractable distributions.The authors say conditioning the original unconditional generative approach on context while retaining prior-noise sampling is suboptimal for this discrete dependency.Source: §1 · p. 2
  • RetroBridge achieves state-of-the-art results on standard retrosynthesis benchmarks as a template-free, single-step method.The paper also reports that its Markov Bridge Model is better suited than a straightforward diffusion-model adaptation to mapping two intractable discrete distributions.Source: §1 · p. 2
  • The Markov Bridge Model learns dependencies between two intractable discrete distributions from finite coupled samples, pinning a process to specific data points at both ends.RetroBridge applies this framework to trajectories from product molecules to data points following the reactant distribution.Source: §1 · p. 2

2 RELATED WORK

Related work spans diffusion and Schrödinger bridge methods, as well as template-based and template-free retrosynthesis systems. The paper positions its contribution at the intersection of discrete distribution mapping and template-free graph-based retrosynthesis.

Diffusion Models

  • Diffusion models have been applied to diverse domains and discrete graphs, but the authors report that diffusion models had not been applied to chemical reaction modeling and retrosynthetic pathway recovery.Source: §2 · pp. 2–3

Schrödinger Bridge Problem

  • Prior Schrödinger bridge work includes unconditional generation and coupled-sample training for continuous distributions, while the authors identify categorical distributions as unaddressed.The Schrödinger bridge problem seeks a process close to a reference process in path-space Kullback-Leibler divergence, given two distributions.Source: §2 · p. 3

Retrosynthesis Modeling

  • Retrosynthesis methods include template-based systems and template-free systems using SMILES, graphs, or both; this work proposes a template-free graph-based method.Source: §2 · p. 3

3 RETROBRIDGE

RetroBridge casts single-step retrosynthesis as learning the dependency between intractable product and reactant distributions from coupled examples. It uses a Markov bridge over molecular graphs and scores generated reactants by model confidence.

3 RETROBRIDGE

  • RetroBridge learns the dependency between intractable product and reactant distributions from a finite collection of coupled product–reactant samples.The framework specializes this approach to single-step retrosynthesis.Source: §3 · p. 3

3.1 MARKOV BRIDGE MODEL

  • A Markov bridge is pinned to product and reactant endpoints; during sampling, φθ(zt, t) approximates y and defines each next-state transition.Training maximizes a lower bound on log qθ(y|x) and minimizes KL divergence between the reference and approximated transition distributions.Source: §3.1 · pp. 3–5

3.2 RETROBRIDGE: MARKOV BRIDGE MODEL FOR RETROSYNTHESIS PLANNING

  • RetroBridge represents products and reactants as molecular graphs with atom-feature nodes and bond-feature edges, adding 10 dummy nodes to each initial product graph.Some dummy nodes become atoms in the final reactant molecules.Source: §3.2 · p. 5

3.3 CONFIDENCE AND SCORING

  • The model ranks generated reactant sets using its confidence, estimated by the likelihood qθ(y|x) for each set given the input product.The likelihood is computed for sets of M samples generated for that product.Source: §3.3 · p. 5

4 RESULTS

On USPTO-50k, RetroBridge outperforms template-free baselines in round-trip evaluation and achieves higher round-trip coverage and accuracy than state-of-the-art template-based methods. It is on par with the state of the art at top-1 exact-match accuracy and leads other template-free methods at higher top-k metrics.

4.1 EXPERIMENTAL SETUP

  • The evaluation uses USPTO-50k with standard train, validation, and test splits; each input product yields 100 sampled reactant sets assessed by exact-match and round-trip metrics.Round-trip accuracy and coverage use Molecular Transformer and account for reactant sets that either match the ground truth or lead back to the input product.Source: §4.1 · p. 6

4.3 RETROSYNTHESIS MODELING

  • RetroBridge matches the state of the art in top-1 exact-match accuracy and outperforms other template-free methods at all other top-k accuracies, especially top-5.The authors identify top-5 accuracy as most relevant to the expected breadth of a multi-step retrosynthesis planning tree and optimize the model for it.Source: §4.3 · pp. 6–7, Table 1 · p. 7
  • RetroBridge achieves higher round-trip coverage and accuracy than state-of-the-art template-based methods, while clearly outperforming template-free baselines.The authors use Molecular Transformer for forward reaction prediction in this evaluation.Source: Table 2 · p. 7, §4.3 · p. 7

4.4 ADDITIONAL EXPERIMENTS

  • Iterative sampling is essential for mapping between graph distributions; the one-shot graph transformer recovered none of the reactants.A single incorrectly predicted bond or atom type can harm exact-match accuracy.Source: §4.4 · p. 8
  • On the USPTO-50k validation set, RetroBridge with context outperforms DiGress with context across all reported metrics; the variational lower-bound loss and per-step product context also help.RetroBridge retains reasonable accuracy without added context, unlike the diffusion approach.Source: §4.4 · p. 8, Table 3 · p. 8

4.5 EXAMPLES

  • In three randomly selected test examples, the top-3 predictions include the correct reactants, and confidence scores reflect uncertainty across cases.The first example has a 0.66 versus 0.12 score gap between its first and second predictions; the other two are less confident.Source: §4.5 · p. 8, Figure 3 · p. 9

5 CONCLUSION

RetroBridge applies the Markov Bridge Model to single-step retrosynthesis and achieves state-of-the-art results on common benchmarks. The conclusion notes practical limitations and possible applications beyond retrosynthesis.

5 CONCLUSION

  • RetroBridge achieves state-of-the-art results on common evaluation benchmarks, and the experiments show that choosing a suitable probabilistic framework improves performance over a straightforward diffusion-model adaptation.The Markov Bridge Model learns dependencies between two intractable discrete-valued distributions.Source: §5 · p. 9
  • RetroBridge does not directly predict experimental conditions or reaction type, and its performance in multi-step planning remains for future assessment.The authors also note that some chemists may prefer template-based planning and propose guiding generation toward specified compounds.Source: §5 · p. 9
  • Markov Bridge Models may also apply to other paired discrete-distribution tasks, including image-to-image translation, inpainting, text translation, and protein-binder design.The authors leave exploration of these applications to future work.Source: §5 · p. 9

A.1 VARIATIONAL LOWER BOUND

The appendix derives a variational lower bound for the log-likelihood of reactants given a product, then expresses its terms using bridge transitions and an unbiased estimator.

A.1 VARIATIONAL LOWER BOUND

  • Jensen’s inequality is used to derive a lower bound on the log-likelihood of reactants given the product, involving bridge-transition terms.The passage identifies the likelihood as that of reactants y ≡ zT given product x ≡ z0.Source: §A.1 · p. 14
  • The initial term L1 is expressed as the negative KL divergence between the bridge distribution p(z1|z0, zT) and qθ(z1|z0)..Source: §A.1 · p. 14
  • Bayes’ rule and the Markov property are used to derive analogous expressions for the intermediate terms Lt from bridge-transition expectations.The displayed steps expand the joint bridge distribution into conditional factors.Source: §A.1 · p. 14
  • The final variational lower bound combines L1 and Lt, replacing the sum over all T terms with an unbiased estimator..Source: §A.1 · pp. 14–15

A.2 CUMULATIVE TRANSITION MATRIX ¯Qt

The appendix proves the stated cumulative transition-matrix form by induction, establishing a base case and carrying the form to the next time step.

A.2 CUMULATIVE TRANSITION MATRIX ¯Qt

  • At t = 0, the proof establishes the base case Q0 = Q0 and α0 = α0..Source: §A.2 · p. 15
  • For t > 0, the induction assumes Qt = αtIK + (1 − αt)y1⊤..Source: §A.2 · p. 15
  • The proof then derives the expression for Qt+1 from the inductive form.The displayed next-step expression is given in the passage.Source: §A.2 · p. 15

A.3.1 NOISE SCHEDULE

The experiments use a cosine noise schedule.

A.3.1 NOISE SCHEDULE

A.3.2 ADDITIONAL FEATURES

The appendix specifies RetroBridge’s molecular graph features, graph-transformer architecture, and training setup, then reports sampling sensitivity and supplementary evaluations.

A.3.2 ADDITIONAL FEATURES

  • The final molecular model represents molecules as fully connected graphs with one-hot atom and bond features, normalized time, global cycle counts through size 6, local counts through size 5, and Laplacian spectral features; it omits molecular weight and valency.Source: §A.3.2 · pp. 15–16

A.3.3 NEURAL NETWORK ARCHITECTURE

  • An MLP encoder feeds Graph Transformer Layers that update nodes through self-attention and FiLM, edges via attention scores, and global features via PNA aggregation; an MLP decoder produces the graph representation.Figure 4 shows the final-state network and a Graph Transformer Layer.Source: §A.3.3 · p. 16, Figure 4 · p. 17

A.3.4 TRAINING

  • Models were trained on one Tesla V100 with AdamW at learning rate 0.0002 and batch size 64 for up to 800 epochs, selecting checkpoints by validation top-5 accuracy.Training took up to 72 hours.Source: §A.3.4 · p. 16

A.3.5 SAMPLING

  • Up to x2 faster sampling leaves performance largely unchanged, but a 5-fold reduction in steps sharply degrades it; using 5-fold fewer samples remains competitive.The step-count test used CE loss on validation data with 50 samples per product; the sample-count test used VLB loss on test data with 500 steps.Source: §A.3.5 · p. 17, Figure 5 · p. 18

A.4 EXTENDED RESULTS

  • Table 4 extends Table 1’s USPTO-50k test exact-match results with additional models and methodological details, distinguishing methods by training-data access and method category.The table caption identifies template-based/template-free and representation categories, and separates methods with more training data or limited vocabularies.Source: §A.4 · p. 18, Table 4 · p. 18

A.5 FORWARD REACTION PREDICTION

  • ForwardBridge achieved performance comparable with other state-of-the-art methods on USPTO-50k and USPTO-MIT, though the probabilistic formulation is less applicable to forward prediction.Figure 6 presents top-3 RetroBridge predictions and confidence scores for 10 random USPTO-50k test inputs, with markers indicating exact matches or forward-model consistency.Source: §A.5 · pp. 18–19, Table 5 · p. 19, Figure 6 · p. 19

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