DeFoG

A graph diffusion model decides how it will be sampled while it is still being trained. The noise schedule, the number of denoising steps and the transition rates are all baked into the training objective, so trying a different sampling procedure means training the network again. One configuration then ends up applied to every dataset, even though a planar mesh, a tree and a drug-like molecule have almost nothing in common structurally.

DeFoG, from EPFL, breaks that coupling. It replaces the diffusion formulation with discrete flow matching: noising follows a straight linear interpolation between the clean graph's one-hot encoding and a reference distribution, and denoising is a continuous-time Markov chain whose rate matrix is specified at inference. Because training only asks the network to predict clean node and edge marginals from a corrupted graph, the whole sampling procedure — a stochasticity level η, a target-guidance weight ω, and a time distortion applied to the step schedule — becomes a set of dials that can be searched against a fixed checkpoint afterwards. The authors relate the training loss to the sampled distribution theoretically, making the decoupling sound rather than merely convenient.

Scope is worth stating plainly: DeFoG is a general attributed-graph generator, not a model pretrained on biology. Its benchmark suite spans synthetic planar, tree, stochastic block model and community graphs alongside molecular and digital-pathology data, and there is no single cross-domain checkpoint — one is trained per dataset. It earns its place here through the molecular and cell-graph checkpoints and their reuse downstream as a frozen generator.

#Key Features

• Training–sampling decoupling: A single trained network supports many inference configurations. η, ω and the time distortion are searched at sampling time, so adapting the sampler to a dataset's structure never requires retraining the denoiser.
• Discrete all the way through: Linear-interpolation noising and CTMC denoising act directly on one-hot node and edge categories, so the model never detours through a continuous relaxation of the adjacency matrix.
• Permutation-equivariant backbone: The denoiser is a graph transformer with multi-head attention over node, edge and graph-level features, augmented with Relative Random Walk Probability encodings that supply structure message passing cannot express.
• Conditional cell-graph generation: In the digital-pathology setting, one conditional model is trained across the low- and high-TLS subsets at once, taking the tissue-content label as the condition instead of fitting a separate model per subset.
• Short refinement trajectories: Because the step schedule is a sampling choice, generation runs at a fraction of the trajectory length the training formulation implies.

#Technical Details

The denoiser follows the graph transformer used by DiGress, predicting clean marginals for every node and edge of a noisy graph. Molecular checkpoints cover QM9 (up to 9 heavy atoms, with and without explicit hydrogens), ZINC250k (249,455 molecules of up to 38 heavy atoms over 9 element types), MOSES (8–27 heavy atoms, drawn from ZINC Clean Leads) and GuacaMol (2–88 heavy atoms, drawn from ChEMBL 24). On GuacaMol the model reaches 99.0% validity and on MOSES 92.8% validity at 99.9% uniqueness; on the synthetic sets it reaches 99.5%, 96.5% and 90% valid-unique-novel graphs for planar, tree and stochastic block model graphs respectively, and still reaches 95.0% and 86.5% on planar and SBM using 5–10% of the sampling steps. The digital-pathology data are cell graphs built by Delaunay triangulation from tissue images, with 9 cell types as node classes and a single edge class; conditioning on low versus high tertiary lymphoid structure content yields 93.0% TLS validity at 50 steps and 95.8% at 1,000 steps. Every reported experiment ran on a single NVIDIA A100-SXM4-80GB GPU.

#Applications

The molecular checkpoints generate valid, novel small-molecule graphs on the standard de novo design benchmarks, suiting screening-library expansion and workflows that need a chemically plausible prior over graphs rather than a property-optimized one. The digital-pathology checkpoint produces synthetic cell graphs conditioned on immune organization, a route to augmenting scarce annotated tissue data. Because the sampler is separable from the network, groups extending the framework to a new biological graph type inherit the sampling-optimization procedure without touching the training code.

#Impact

DeFoG was presented as an oral at ICML 2025 and has been taken up as infrastructure rather than only as a benchmark entry: DBMol uses a pretrained DeFoG checkpoint as its frozen molecular generator, steering it with gradients from a separate affinity model, and the same lab has extended the framework to directed graphs. The wider contribution is methodological: the sampler of a discrete graph generative model can be treated as a searchable object after training, turning per-dataset adaptation from a training cost into an inference cost. The limitation for biological users is that checkpoints are dataset-specific — there is no general pretrained graph model here, and a new corpus still requires training the denoiser from scratch.