SynBridge: Bidirectional Reaction Model

• SynBridge is a bidirectional, flow-based generative model that models multi-task chemical reaction prediction by interpolating discrete molecular graph states.
• It leverages a graph-to-graph Transformer framework to encode and decode the reactant and product graphs for both synthesis and retrosynthesis tasks.
• Its innovative discrete flow bridge formulation with balanced noise scheduling enables accurate simulation of chemical transformations, achieving state-of-the-art benchmark results.

SynBridge is a bidirectional, flow-based generative model designed for multi-task chemical reaction prediction, explicitly modeling the inherently discrete changes in atoms and bonds during chemical transformations. The architecture leverages a discrete flow bridge to interpolate continuously in time between discrete reactant and product molecular graph distributions. By employing a graph-to-graph Transformer framework, SynBridge captures bidirectional chemical transformations, enabling both forward synthesis and retrosynthesis while achieving state-of-the-art results on several reaction benchmarks (Lin et al., 11 Jul 2025).

1. Discrete Chemical State Modeling

Chemical reactions involve non-continuous changes such as electron transfer, bond formation/breaking, and alterations in atomic charge states. SynBridge formulates the reaction process as a bidirectional translation between two molecular graphs: the reactant graph ($\mathcal{G}_-$, source) and the product graph ($\mathcal{G}_+$, target). Each graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ is described by:

• Atom-level discrete variables:
  • Atom type $a^{(i)} \in \{1,\dots,M\}$, with one dummy type for atom deletion/appearance.
  • Aromaticity indicator $b^{(i)} \in \{0,1\}$.
  • Formal charge $c^{(i)} \in \{-6,\dots,+6\}$.
• Bond-level discrete variables:
  • Entries $r^{(ij)} \in \{0,1,2,3\}$ in adjacency matrix $R$, denoting nonbonded, single, double, and triple bonds.

SynBridge's central innovation is the Discrete Flow Bridge, which defines a continuous-time interpolation $p_t$ between the endpoint discrete distributions $p_0$ (reactants) and $\mathcal{G}_+$0 (products) for each variable $\mathcal{G}_+$1:

$\mathcal{G}_+$2

where $\mathcal{G}_+$3 is the Kronecker delta, $\mathcal{G}_+$4 is the uniform distribution over $\mathcal{G}_+$5 classes, and coefficients $\mathcal{G}_+$6 satisfy specific boundary and normalization constraints. This forms the basis for time-dependent transport between reactant and product states, supporting both synthesis directions.

2. Graph-to-Graph Transformer Architecture

SynBridge parameterizes conditional distributions $\mathcal{G}_+$7 with a modular graph-to-graph Transformer $\mathcal{G}_+$8, structured as:

• MolEncoder: Processes atom-level embeddings for $\mathcal{G}_+$9 via linear layers summed to $\mathcal{G} = (\mathcal{V}, \mathcal{E})$0. Bond information is integrated ($\mathcal{G} = (\mathcal{V}, \mathcal{E})$1), and a stack of $\mathcal{G} = (\mathcal{V}, \mathcal{E})$2 TransformerEncoder layers implements self-attention, yielding $\mathcal{G} = (\mathcal{V}, \mathcal{E})$3. Both the source graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$4 and the current noisy graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$5 are encoded separately and summed:

$\mathcal{G} = (\mathcal{V}, \mathcal{E})$6

• MergeEncoder: Incorporates a learnable task token $\mathcal{G} = (\mathcal{V}, \mathcal{E})$7 (forward/retro) lifted to $\mathcal{G} = (\mathcal{V}, \mathcal{E})$8. $\mathcal{G} = (\mathcal{V}, \mathcal{E})$9 layers of cross-attention Transformer blocks use $a^{(i)} \in \{1,\dots,M\}$0 as query and $a^{(i)} \in \{1,\dots,M\}$1 as key/value, producing $a^{(i)} \in \{1,\dots,M\}$2.
• MolDecoder: Processes $a^{(i)} \in \{1,\dots,M\}$3 through $a^{(i)} \in \{1,\dots,M\}$4 Transformer layers, outputting $a^{(i)} \in \{1,\dots,M\}$5, which feeds four parallel heads for predicting atom type, aromaticity, charge, and bonds via softmaxed logits.

Training utilizes cross-entropy losses against ground-truth graphs for both reaction directions, with multi-tasking handled via $a^{(i)} \in \{1,\dots,M\}$6.

3. Discrete Flow Bridge Formulation and Training

The flow bridge defines a family of marginals $a^{(i)} \in \{1,\dots,M\}$7 and associated instantaneous probability velocities $a^{(i)} \in \{1,\dots,M\}$8 based on discrete flow matching theory:

$a^{(i)} \in \{1,\dots,M\}$9

with $b^{(i)} \in \{0,1\}$0.

Learning is driven by minimizing:

• Forward direction (reactant→product):

$b^{(i)} \in \{0,1\}$1

• Reverse direction (product→reactant):

$b^{(i)} \in \{0,1\}$2

The losses are combined multi-task via the task token. Noise injection, governed by the schedule

$b^{(i)} \in \{0,1\}$3

($b^{(i)} \in \{0,1\}$4), provides a balanced degree of stochasticity, ensuring the bridge does not prematurely collapse to either endpoint.

4. Multi-Task Reaction Prediction Process

SynBridge implements multi-task learning, randomly choosing task direction at each iteration using the $b^{(i)} \in \{0,1\}$5 token. The model predicts either forward (synthesis) or reverse (retrosynthesis) over cleaned, atom-mapped input graphs, without explicit reagent or catalyst information. The sampling procedure for graph generation is conducted via an ODE-style Euler solver over $b^{(i)} \in \{0,1\}$6 in $b^{(i)} \in \{0,1\}$7 discrete steps:

$b^{(i)} \in \{0,1\}$8

Bidirectionally, this enables SynBridge to serve both major tasks in reaction prediction within a unified framework.

5. Experimental Results and Comparative Analysis

Performance is evaluated on three reaction datasets:

Dataset	Size (train/val/test)	Notable Features
USPTO-50K	40k/5k/5k	No ionic species
USPTO-MIT	$b^{(i)} \in \{0,1\}$9480k	Includes ionic species and charge information
Pistachio	$c^{(i)} \in \{-6,\dots,+6\}$02.8M raw, 478k filtered	High structural diversity and charge diversity

The primary evaluation metric is Top-$c^{(i)} \in \{-6,\dots,+6\}$1 accuracy (SMILES match from predicted atom/bond states). SynBridge is compared to baselines including MEGAN, NeRF, RetroBridge, T5Chem, G2G-Former, and S2S-Former. Results (Top-1 / Top-3 / Top-5, %):

Task/Dataset	SynBridge	Baseline
USPTO-50K forward	95.9 / 96.2 / 96.5	S2S-Former 95.0 / 95.2 / 95.8
USPTO-50K retro	79.4 / 84.4 / 85.7	G2G-Former 53.8 / 77.0 / 79.2
USPTO-MIT forward	88.4 / 90.1 / 92.4	NeRF 87.1 / 88.8 / 89.1
USPTO-MIT retro	37.8 / 40.1 / 41.5	G2G-Former 25.6 / 32.8 / 34.6
Pistachio forward	94.8 / 97.4 / 98.0	NeRF 92.2 / 94.6 / 95.9
Pistachio retro	66.1 / 75.0 / 79.3	G2G-Former 55.6 / 66.5 / 66.7

On multi-task retrosynthesis (Pistachio Top-1): SynBridge 71.5%, T5Chem 67.4%. Improvements of 2–10 percentage points across tasks are statistically significant ($c^{(i)} \in \{-6,\dots,+6\}$2, paired bootstrap, 1000 resamples) (Lin et al., 11 Jul 2025).

6. Ablation Studies and Model Analysis

Systematic ablations on USPTO-MIT forward prediction demonstrate:

• Role of Initial Graph Input: Excluding $c^{(i)} \in \{-6,\dots,+6\}$3 from $c^{(i)} \in \{-6,\dots,+6\}$4 reduces Top-1 accuracy from 88.4% to 66.4%, indicating the necessity of source graph context for message passing.
• Effect of Uniform Noise Level $c^{(i)} \in \{-6,\dots,+6\}$5 (20 steps):
  • $c^{(i)} \in \{-6,\dots,+6\}$6, $c^{(i)} \in \{-6,\dots,+6\}$7, $c^{(i)} \in \{-6,\dots,+6\}$8, $c^{(i)} \in \{-6,\dots,+6\}$9.
  • Insufficient noise causes model over-confidence and early errors; excessive noise reduces signal quality.
• Sampling Steps (with $r^{(ij)} \in \{0,1,2,3\}$0):
  • $r^{(ij)} \in \{0,1,2,3\}$1, $r^{(ij)} \in \{0,1,2,3\}$2, $r^{(ij)} \in \{0,1,2,3\}$3, $r^{(ij)} \in \{0,1,2,3\}$4.
  • Increasing steps enables self-correction, with performance plateauing beyond 20–50 steps.

Key findings include the need for both endpoint context and carefully balanced noise scheduling for robust discrete bridge generation, and superior performance of multi-step bridging over one-step direct mappings, especially for retrosynthesis.

7. Context and Significance

SynBridge introduces a principled framework for modeling chemical reaction state transitions as discrete, bidirectional flows, unifying forward synthesis and retrosynthesis tasks in a single architecture and training objective. The discrete flow bridge formulation addresses the fundamental challenge of the non-continuous nature of chemical changes, surpassing prior one-step and diffusion-based architectures in both accuracy and bidirectionality. The approach demonstrates applicability across reaction types, molecular charge states, and dataset diversity, and establishes new benchmarks for data-driven reaction prediction (Lin et al., 11 Jul 2025).