Latent Flow Matching for Molecular Graph Generation

Mathis Goupillon; Roman Bresson; Konstantinos Divriotis; Michalis Vazirgiannis

cs.LGOct 5, 2026

Latent Flow Matching for Molecular Graph Generation

Authors: Mathis Goupillon, Roman Bresson, Konstantinos Divriotis, Michalis Vazirgiannis

Organizations: Mohamed bin Zayed University of Artificial Intelligence

Abstract

Modern graph generative models typically operate directly in the discrete graph space, explicitly generating node and edge variables, which can become costly as graphs grow. In this paper, we perform generation explicitly on latent representations of entire graphs obtained from a pretrained Variational Autoencoder with high reconstruction fidelity. The generated representations, obtained through flow matching, are then decoded only at the final step. Across molecular benchmarks of increasing size, our approach achieves strong validity and FCD while offering a favorable quality-efficiency trade-off compared with state-of-the-art explicit graph generative models. One of the main advantages of this formulation is that the graph representation only needs to be learned once, after which the same one can be reused across multiple generative objectives without retraining. We demonstrate generation guided by molecular properties and further introduce validity-aware generation though a classifier learned directly in latent space. All code will be made available upon acceptance.

Figures & tables

Panel of Figure 1 — Figure 1 : Overview of latent graph generation and validity-guided sampling. Top: latent flow matching; Bottom: construction of the validity dataset and validity predictor training.

Name	# Graph	# atom	# bonds	Max Size	Atom types	Emb. Dim.
QM9	$130$ k	$8.79$	$9.4$	$9$	$4$	$64$
PubChem16	$12.89$ M	$13.87$	$14.19$	$16$	$31$	$256$
PubChem32	$74.34$ M	$21.75$	$21.15$	$32$	$31$	$512$

Table 1 : Statistics of the used datasets. Numbers of atoms and bonds are reported on average. Last column is the dimension of the latent representation.

Method	Sampler	NFE	Validity $\uparrow$	Uniq. $\uparrow$	Novelty $\uparrow$	FCD $\downarrow$	Time (s) $\downarrow$	VUN/T $\uparrow$
QM9
DiGress	Diffusion	2	$47.3\pm 1.4$	$97.5\pm 0.9$	N/A	$3.420$	$0.324\pm 0.081$	$1457.5$
DiGress	Diffusion	5	$76.7\pm 1.7$	$99.5\pm 0.3$	N/A	$1.150$	$0.633\pm 0.005$	$1234.6$
DiGress	Diffusion	20	$97.8\pm 0.4$	$\textbf{99.7}\pm 0.2$	N/A	$0.087$	$2.275\pm 0.030$	$438.9$
DiGress	Diffusion	500	$\textbf{99.9}\pm 0.1$	$99.6\pm 0.2$	N/A	0.061	$54.801\pm 0.13$	$18.6$
CFM-CSD	CSD	1	$94.6\pm 0.6$	$98.6\pm 0.6$	N/A	$1.873$	$0.391\pm 0.005$	$2442.8$

Table 2 : Unconditional generation results on our three benchmarks. Validity, novelty and uniqueness are reported as mean

\pm

standard deviation over 20 runs of 1,024 molecules. FCD is computed over the generated set. Time denotes end-to-end generation of 1,024 molecules and includes the VAE decoding for our method. NFE stands for number of function evaluations (1 per step for Euler, 2 per step for midpoint and Heun solver). The numerical solvers are detailed in Appendix E.3 . Our approaches are Latent FM, Latent FM with validity guidance (VG) and Validity-Aware VFM (VA-VFM). Qualitative examples of pc32 generation are provided in Appendix F .

Method / component	QM9	PubChem16
DiGress	7 h 34 min	16 h 55 min
CFM-CSD	63 h 49 min	73 h 21 min
CFM-ECLD	70 h 53 min	71 h 40 min
Latent FM	27 min	3 h 50 min
Validity dataset construction	2 h 06 min	8 h 05 min
Validity predictor	1 min 28 s	1 min 12 s

Table 3 : Single-GPU training cost on QM9 and PubChem16. Times for the proposed methods assume a fixed pretrained graph representation and therefore exclude the one-time encoder-decoder pretraining cost.

Panel of Figure 2 — Figure 2 : Independent property-controlled generation on QM9 and PubChem16. Points show the mean property of generated molecules for each requested target, with error bars indicating one standard deviation. The dashed line corresponds to ideal control, while the shaded region indicates the 5-95% range of the training distribution.

Dataset	Property	Conditional FM		+ Guidance
		MAE $\downarrow$	$\mathbf{r}$ $\uparrow$	MAE $\downarrow$	$\mathbf{r}$ $\uparrow$
QM9	logP	0.100	0.978	0.063	0.988
QM9	MW	1.705	0.979	1.674	0.981
PubChem16	logP	0.282	0.966	0.154	0.978
PubChem16	MW	3.040	0.976	2.578	0.977

Table 4 : Effect of gradient-based property guidance on target fidelity. We compare conditional flow matching (CFM) with CFM augmented with property-predictor guidance. Lower MAE and higher Pearson correlation

r

indicate better property control.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 3 — Figure 3 : Independent property-controlled generation in the deterministic GraViti AE latent space on PubChem16. Generated properties are shown as a function of the requested target for logP and molecular weight. The dashed line denotes ideal control ( $y=x$ ), and the shaded region indicates the corresponding training-distribution range.

Panel of Figure 4 — Figure 4 : Validity and uniqueness as a function of the target property for property-guided molecular generation on QM9 and PubChem16.

Method	Steps	Validity $\uparrow$	Uniqueness $\uparrow$	Novelty $\uparrow$	FCD $\downarrow$
CFM-CSD	1	$88.19\pm 1.11$	$99.51\pm 0.23$	$75.10\pm 1.30$	$6.8832$
CFM-CSD	2	$86.48\pm 0.97$	$99.98\pm 0.07$	$87.03\pm 1.01$	$2.5352$
CFM-CSD	5	$93.85\pm 0.75$	$100.00\pm 0.00$	$88.58\pm 0.93$	$1.4919$
CFM-CSD	20	$97.58\pm 0.51$	$99.99\pm 0.02$	$88.77\pm 1.00$	$0.9430$
CFM-ECLD	1	$96.02\pm 0.55$	$98.87\pm 0.35$	$64.62\pm 1.47$	$6.8654$
CFM-ECLD	2	$94.45\pm 0.64$	$99.96\pm 0.06$	$85.91\pm 1.27$	$2.6004$

Appendix

Table 5 : Unconditional generation results for CFM-CSD and CFM-ECLD on PubChem16 after 30 training epochs (

\sim

107 GPU hours). Validity, uniqueness, and novelty are reported as mean

\pm

standard deviation.

Dataset	Property	Validity $\uparrow$	Uniqueness $\uparrow$
QM9	logP	$0.9873$	$0.996$
QM9	MW	$0.9824$	$0.998$
PubChem16	logP	$0.9277$	$1.000$
PubChem16	MW	$0.9268$	$1.000$

Appendix

Table 6 : Global validity and uniqueness under property-guided generation. Target properties are sampled according to their empirical training distribution before generating the corresponding molecules.

Panel of Figure 5 — Figure 5 : Qualitative examples of molecules generated on PubChem32 by DiGress (top) and our Flow Matching model (bottom).

Figure 6 : Examples of molecules generated with property-guided latent Flow Matching on QM9 and PubChem16 for logP and molecular weight (MW) targets. Examples are shown for both in-distribution and out-of-distribution target values. The achieved property value is reported below each generated molecule.

Representation	Property	MAE $\downarrow$	$\mathbf{r}$ $\uparrow$
AE	logP	0.247	0.966
VAE	logP	0.154	0.978
AE	MW	3.923	0.971
VAE	MW	2.578	0.977

Appendix

Table 7 : Effect of the graph-level latent representation on independent property control on PubChem16. Both representations are evaluated using the same guidance protocol.

Hyperparameter	QM9NoHydro	PubChem16
Latent dimension	64	256
Latent transform (FM)	None	Standardization
Flow Matching
Hidden dimension	1024	2048
Number of layers	6	10
Time embedding dimension	1	64

Appendix

Table 8: Hyperparameters used for the models retained in our experiments.

Hyperparameter	QM9 MW	QM9 logP
Latent dimension	64	64
Conditioning property	MW	logP
Property normalization	Standardized	Standardized
Latent transform	None	None
Conditional Flow Matching
Hidden dimension	512	512

Appendix

Table 9: Hyperparameters used for property-guided generation on QM9NoHydro. Conditioning properties are standardized using training-set statistics. No latent transformation is applied.

Hyperparameter	PubChem16 MW	PubChem16 logP
Latent dimension	256	256
Conditioning property	MW	logP
Property normalization	Standardized	Standardized
Latent transform	None	None
Conditional Flow Matching
Hidden dimension	1024	1024

Appendix

Table 10: Hyperparameters used for property-guided generation on PubChem16. Conditioning properties are standardized using training-set statistics. No latent transformation is applied.

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Molecular graph generation (MGG) is essentially a multi-class generative task, aimed at predicting categories of atoms and bonds under strict chemical and structural constraints. However, many prevailing diffusion paradigms learn to regress numerical embeddings and rely on a hard discretization rule during sampling to recover discrete labels. This introduces a fundamental discrepancy between training and sampling. While models are trained for point-wise numerical fidelity, the sampling process fundamentally relies on crossing categorical decision boundaries. This discrepancy forces the model to expend efforts on intra-class variations that become irrelevant after discretization, ultimately compromising diversity, structural statistics, and generalization performance. Therefore, we propose TopBF, a unified framework that (i) performs MGG directly in continuous parameter distributions, (ii) learns graph-topological understanding through a Quasi-Wasserstein optimal-transport coupling under geodesic costs, and (iii) supports controllable, property-conditioned generation during sampling without retraining the base model. TopBF innovatively employs cumulative distribution function (CDF) to compute category probabilities induced by the Gaussian channel, thereby unifying the training objective with the sampling discretization operation. Experiments on QM9 and ZINC250k demonstrate superior structural fidelity and efficient generation with improved performance.

Abstract

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