CSGD

CSGD (Composable Score-based Graph Diffusion) is a generative model for molecular graphs that must satisfy several property constraints at once. Design campaigns rarely ask for a single objective: a polymer candidate may need target ranges for synthetic accessibility and for the permeability of three different gases, while a drug candidate may need blood-brain-barrier penetration alongside a tractable synthesis route. Most graph diffusion generators collapse every property into one joint condition, which makes the influence of individual properties opaque and fixes the condition set at training time.

CSGD, developed by Anjie Qiao, Zhen Wang and Chuan Chen at Sun Yat-sen University with Defu Lian and Enhong Chen at the University of Science and Technology of China and posted to arXiv in September 2025, takes a different route. It extends score matching to discrete molecular graphs through the concrete score — the ratio between the probabilities of neighboring discrete states — rather than the mean-prediction objective used by earlier discrete graph diffusion models. Because scores are additive, per-property guidance terms can be combined algebraically, which is what makes conditions composable.

Two techniques build on that foundation. Composable Guidance (CoG) estimates a separate conditional score for each property and merges them at sampling time, so one checkpoint can be steered by any subset of the properties it was trained on. Probability Calibration (PC) reshapes the estimated transition probabilities during denoising, reducing the train-test mismatch that degrades chemical validity. CSGD sits alongside controllable graph-diffusion generators such as CoMole and DemoDiff, but targets composability of the guidance signal itself rather than adaptation to unseen properties.

#Key Features

• Concrete-score formulation for discrete graphs: Extends score matching from continuous data to discrete graph states, avoiding the continuous relaxation that predictor-guided models rely on and that costs generation fidelity.
• Composable Guidance (CoG): Trains per-property and unconditional score functions jointly, then combines them at inference, letting one model be conditioned on the full property set, a single property, or any mixed subset without retraining.
• fast-CoG for efficiency: An alternative training strategy pools condition embeddings so a subset score takes one network evaluation instead of one per property, keeping inference cost near-constant as conditions are added.
• Probability Calibration (PC): A plug-in adjustment to estimated transition probabilities that improves both validity and controllability under classifier-free and composable guidance alike.
• Mixed categorical and numerical conditioning: Separate encoders handle binary activity labels and continuous property vectors, with condition dropout during training supplying the unconditional score.

#Technical Details

The denoiser is a permutation-equivariant Graph Transformer over node and edge tokens, adopted with minor changes from the GraphDiT architecture, while the diffusion machinery follows the SEDD implementation with a log-linear noise schedule in a discrete-state, continuous-time setting. Training used 1,000 diffusion steps, a batch size of 1,200, a learning rate of 3x10⁻⁴, gradient clipping at norm 1, and a 1,500-iteration linear warm-up; each dataset trains in under 24 hours on a single NVIDIA A800 80GB GPU.

Evaluation covers four corpora, each trained separately: a Polymers dataset with four numerical conditions (a synthesizability vector combining SAS and SCS, plus O₂, N₂ and CO₂ permeability) and the class-balanced BACE, BBBP and HIV sets from MoleculeNet, each pairing that vector with a binary activity label. Data are split 6:2:2 and 10,000 molecules generated per condition set, scored with MOSES distributional metrics and a random-forest oracle for property compliance. On Polymers, CSGD improves average MAE by 15.3% over the strongest baseline. On HIV it reaches 83.4% validity and 0.990 property accuracy against 69.1% and 0.944 for GraphDiT; on BBBP, 95.6% and 0.983 against 78.7% and 0.909; on BACE, 96.9% and 0.925.

#Applications

The immediate use cases are multi-objective design campaigns where the objective set changes between runs. In materials work, that means proposing polymer repeat units that hit gas-permeability targets for membrane separation while staying synthetically accessible. In drug discovery, it means enumerating candidate scaffolds predicted to inhibit a target such as beta-secretase 1 or HIV replication while remaining tractable to make, then re-querying the same checkpoint with a narrower or broader property set as priorities shift. Because guidance is composed at sampling time, objective trade-offs can be explored without a new training run.

#Impact

CSGD is a preprint and has not yet been peer reviewed. Its main contribution is methodological: showing that the concrete score, introduced for discrete language diffusion, transfers to molecular graphs and unlocks score-manipulation techniques that mean-prediction graph diffusion models cannot use. Two limitations bound its reach. Each benchmark is trained as its own checkpoint, so this is a task-specific generator rather than a broadly pretrained chemical foundation model, and all controllability numbers come from random-forest oracles rather than experimental measurement. The paper names a GitHub repository as the home for its code and data, but that repository is not publicly accessible, and no weights or license have been released.