Diffusion-based Evolutionary Optimization for 3D Multi-Objective Molecular Generation

Ruiqing Sun; Dawei Feng; Sen Yang; Ronghang Wang; Huaiyuan Song; Bo Ding; Yijie Wang; Huaimin Wang

cs.NEMay 16, 2025

Diffusion-based Evolutionary Optimization for 3D Multi-Objective Molecular Generation

Authors: Ruiqing Sun, Dawei Feng, Sen Yang, Ronghang Wang, Huaiyuan Song, Bo Ding, Yijie Wang, Huaimin Wang

Organizations: College of Computer Science and Technology, National University of Defense Technology, 410073, Changsha, China · Bioinformatics Center, Academy of Military Medical Sciences (AMMS), 100080, Beijing, China

Abstract

De novo 3D molecular design with multiple properties and fragment-retention constraints is formulated as a constrained multi-objective optimization problem. Existing 3D diffusion models provide strong capabilities for generating novel molecules, but adapting them to new conditions and multi-objective optimization tasks remains difficult. We present Diffusion-based Evolutionary Molecular Optimization (DEMO), a framework that draws solely on the unconditional molecular prior of a frozen pretrained diffusion model to generate chemically valid 3D candidates, while evolutionary search handles conditional generation and constrained multi-objective optimization, without retraining or fine-tuning. DEMO performs crossover and mutation on intermediate diffusion states through an Evolutionary-Guided Diffusion (EGD) operator, combines 2D topology and 3D geometry in Structure-Aware Environmental Selection (SAES) to preserve structural diversity, and uses three cooperating populations to coordinate structural exploration, fragment-constraint satisfaction, and property optimization. Experimental results demonstrate that EGD outperforms task-specific conditional generators in property targeting; SAES preserves structural diversity while retaining competitive hypervolume in multi-objective optimization; and DEMO improves objective convergence and generates diverse feasible molecules under fragment constraints. These results show how evolutionary search can reuse existing diffusion models for diverse molecular design requirements.

Figures & tables

Fig. 1: Illustration of single-objective optimization (SOP, left) and multi-objective optimization (MOP, right). SOP converges to one target solution. MOP progresses toward the feasible region and approximates the Pareto front.

Fig. 2: Overall architecture of the DEMO framework.

Fig. 3: Effect of the noise level

t^{\prime}

on EGD offspring quality on QM9. Molecular validity and atom stability increase rapidly before reaching a plateau.

Fig. 4: Effect of molecular size

N

on noise robustness (GEOM-Drugs). The validity knee point shifts toward larger

t^{\prime}

as molecular size increases, with consistent trends for GeoLDM and EDM.

Panel of Figure 5 — Fig. 5: Search trajectories for simultaneous optimization of $\alpha$ and $\Delta\varepsilon$ . Gray points denote 100,000 molecules sampled from the unconditional model. Top-N remains concentrated in the high-density region, whereas the evolutionary methods progressively approach the Pareto boundary. Compared with SPEA2, SAES maintains a more structurally diverse set of solutions along the front.

Method	$\alpha$	$\Delta\varepsilon$	$\varepsilon_{\text{homo}}$	$\varepsilon_{\text{lumo}}$	$\mu$	$C_{v}$
cEDM	2.76	655	356	584	1.11	1.10
cGeoLDM	2.37	587	340	522	1.11	1.03
EEGSDE	2.50	487	302	447	0.78	0.94
cGCDM	1.99	595	346	480	0.86	0.70
PropMolFlow	1.36	391	246	312	0.63	0.64
NExT-Mol	1.16	297	205	235	0.51	0.51

TABLE I: MAE (

\downarrow

) on Single-Property Targeting tasks.

Backbone: GeoLDM
Task	Prop.	Baselines			Top-N		EGD & Ablation
Task	Prop.	MUDM	EEGSDE	Base	(SE)	(SR)	w/o CO	w/o MT	Ours
$C_{v}/\mu$	$C_{v}$	1.47	0.98	1.23	1.21	2.25	0.64	1.67	0.69
$C_{v}/\mu$	$\mu$	0.69	0.91	1.12	0.34	0.59	0.28	0.29	0.09
$\Delta\varepsilon/\mu$	$\Delta\varepsilon$	544	563	664	234	461	78	228	186
$\Delta\varepsilon/\mu$	$\mu$	0.58	0.87	1.13	0.31	0.54	0.25	0.27	0.48

TABLE II: MAE (

\downarrow

) on the Multi-Property Targeting task.

Task	HV D	HV 100K	GeoLDM							EDM
			Top-N		EGD Ablation & Selection					Top-N		EGD Ablation & Selection
			(SR)	(SE)	w/o CO	w/o MT	SPEA2	SPEA2-SD	SAES	(SR)	(SE)	w/o CO	w/o MT	SPEA2	SPEA2-SD	SAES
$\alpha$ – $\Delta\varepsilon$	0.854	0.802	0.559 (0.017) $-$	0.590 (0.024) $-$	0.568 (0.054) $-$	0.760 (0.015) $=$	0.758 (0.019) $=$	0.759 (0.017)	0.764 (0.016)	0.535 (0.016) $-$	0.629 (0.029) $-$	0.545 (0.042) $-$	0.761 (0.012) $=$	0.766 (0.012) $-$	0.769 (0.016)	0.772 (0.019)
$\alpha$ – $\Delta\varepsilon$	0.854	0.802	[0.997]	[1.000]	[0.734]	[0.895]	[0.312]	[0.278]	[0.896]	[1.000]	[1.000]	[0.698]	[0.932]	[0.300]	[0.277]	[0.880]
$\Delta\varepsilon$ – $\varepsilon_{\mathrm{ho}}$	0.702	0.678	0.461 (0.020) $-$	0.543 (0.015) $-$	0.489 (0.042) $-$	0.644 (0.019) $=$	0.635 (0.018) $-$	0.637 (0.027)	0.639 (0.018)	0.475 (0.020) $-$	0.536 (0.026) $-$	0.478 (0.036) $-$	0.641 (0.020) $=$	0.640 (0.017) $=$	0.648 (0.024)	0.640 (0.017)
$\Delta\varepsilon$ – $\varepsilon_{\mathrm{ho}}$	0.702	0.678	[0.982]	[1.000]	[0.776]	[0.962]	[0.251]	[0.247]	[0.876]	[1.000]	[1.000]	[0.725]	[0.951]	[0.276]	[0.231]	[0.871]

TABLE III: HV (

\uparrow

) and UVR (

\uparrow

) on unconstrained multi-objective optimization. Values in square brackets denote UVR. Symbols (

+

-

=

) indicate the statistical significance of HV relative to the full SAES method.

HV_{D}

and

HV_{100K}

denote the HV of the reference dataset and 100,000 unconditional samples, respectively.

Fig. 6: Structural diversity and convergence across all MOP tasks on EDM. (a) Internal Tanimoto diversity, (b) the number of distinct Bemis–Murcko scaffolds, (c) median 3D MCS RMSD, and (d) hypervolume. Lines are means across the ten tasks and shading is the standard deviation across tasks. SPEA2-SD replaces only the objective-space density term with structural distance and follows the SPEA2 diversity trajectory. SAES maintains higher structural diversity while its hypervolume stays competitive.

Fig. 7: Comparison between direct crossover in the GeoLDM latent space and EGD in the noise space. (a) Chemical validity and stability of unscreened offspring across three noise levels. (b) Hypervolume after search on the

\alpha

–gap and gap–LUMO–

C_{v}

tasks. Paired seeds are connected by lines, and open markers indicate seed means.

Backbone: GeoLDM
Target	Top-N (SE)	Evolutionary Framework
Target	Unconditional	SPEA2	SAES (Ours)
4tqr	0.718 (.080) $-$ - 1.00	0.798 (.095) $=$ - 0.84	0.793 (.081) - 0.97
1k9t	0.339 (.038) $=$ - 0.60	0.338 (.028) $=$ - 0.47	0.328 (.018) - 0.64
1ai4	0.458 (.033) $-$ - 0.95	0.481 (.043) $-$ - 0.71	0.490 (.049) - 0.92
5mgl	0.485 (.039) $-$ - 0.91	0.517 (.043) $-$ - 0.65	0.519 (.038) - 0.87

TABLE IV: Extended HV (

\uparrow

) and UVR (

\uparrow

) results on the 3D Protein-Ligand Docking MOP task. Values are formatted as HV(Std) - UVR .

Task	Top-N	Traditional CMOEAs			Ablation & DEMO			Task	Top-N	Traditional CMOEAs			Ablation & DEMO
Task	(SE)	SPEA2	CCMO	CMOEA-CD	w/o Pop B	Only Pop C	Ours	Task	(SE)	SPEA2	CCMO	CMOEA-CD	w/o Pop B	Only Pop C	Ours
Backbone: GeoLDM								Backbone: EDM
$\alpha$ — $\Delta\varepsilon$	0.035 (.085) $-$	0.352 (.023) $-$	0.343 (.028) $-$	0.338 (.033) $-$	0.399 (.042) $=$	0.386 (.062) $=$	0.394 (.036)	$\alpha$ — $\Delta\varepsilon$	0.104 (.014) $-$	0.141 (.137) $=$	0.111 (.133) $-$	0.093 (.012) $-$	0.091 (.143) $-$	0.182 (.136) $=$	0.143 (.147)
$\alpha$ — $\Delta\varepsilon$	[0.04/0.01]	[1.00/0.13]	[1.00/0.17]	[1.00/0.18]	[1.00/0.46]	[0.15/0.11]	[1.00/0.53]	$\alpha$ — $\Delta\varepsilon$	[0.01/0.01]	[0.47/0.05]	[0.31/0.03]	[0.31/0.02]	[0.24/0.03]	[0.03/0.03]	[0.44/0.03]
- $\Delta\varepsilon$ – $\varepsilon_{\text{ho}}$	0 (.0) $-$	0.015 (.069) $-$	0.011 (.048) $-$	0.025 (.077) $=$	0.024 (.081) $=$	0 (.0) $-$	0.025 (.067)	- $\Delta\varepsilon$ – $\varepsilon_{\text{ho}}$	0.251 (.068) $-$	0.297 (.084) $-$	0.316 (.038) $-$	0.297 (.074) $-$	0.358 (.047) $=$	0.358 (.044) $=$	0.356 (.044)
- $\Delta\varepsilon$ – $\varepsilon_{\text{ho}}$	[0.00/0.00]	[0.05/0.01]	[0.05/0.01]	[0.10/0.01]	[0.01/0.01]	[0.00/0.00]	[0.10/0.01]	- $\Delta\varepsilon$ – $\varepsilon_{\text{ho}}$	[0.12/0.11]	[0.95/0.11]	[0.96/0.12]	[0.95/0.15]	[1.00/0.34]	[0.11/0.11]	[1.00/0.42]

TABLE V: Comprehensive HV (

\uparrow

) and [FR

\uparrow

/ UFR

\uparrow

] results on the CMOP multi-fragment generation task.

Fig. 8: UFR and HV on the

\varepsilon_{\mathrm{ho}}

–

\varepsilon_{\mathrm{lu}}

task.

Panel of Figure 14 — Fig. 9: Additional CMOP visualization results across different property combinations and diffusion backbones. DEMO optimizes the conflicting properties while retaining the specified target fragment substructures. (1) $\alpha$ , $\varepsilon_{\mathrm{ho}}$ , and $\mu$ with GeoLDM; (2) $\varepsilon_{\mathrm{lu}}$ and $\mu$ with EDM;

Fig. 10: Ablation of the SAES structural-distance threshold

\tau

on the EDM HOMO–LUMO fragment-constrained task. (a) Final hypervolume and (b) unique feasible rate. Error bars denote the sample standard deviation.

Fig. 11: Share of the wall-clock time of one run, averaged over five repeats; numbers above the bars are rounded mean minutes per run. Task abbreviations: Pair, MOP, and CMOP are

\varepsilon_{\mathrm{ho}}

–

\varepsilon_{\mathrm{lu}}

tasks; Dock is docking; Geo is GeoLDM. Top-N, QM9 denotes unconditional Top-

N

sampling on the

\varepsilon_{\mathrm{ho}}

–

\varepsilon_{\mathrm{lu}}

fragment-constrained task with the EDM backbone, and Top-N, Dock its counterpart on docking. Each bar is divided into Diffusion (reverse diffusion), Docking (pose scoring), Evaluation (property, chemical, and fragment checks), Search (crossover, noising, selection, and adaptive scheduling), and Other (model loading, initial sampling, and unlisted overhead).

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Goal-directed molecular generation requires satisfying heterogeneous constraints such as protein--ligand compatibility and multi-objective drug-like properties, yet existing methods often optimize these constraints in isolation, failing to reconcile conflicting objectives (e.g., affinity vs. safety), and struggle to navigate the non-differentiable chemical space without compromising structural validity. To address these challenges, we propose CAGenMol, a condition-aware discrete diffusion framework over molecular sequences that formulates molecular design as conditional denoising guided by heterogeneous structural and property signals. By coupling discrete diffusion with reinforcement learning, the model aligns the generation trajectory with non-differentiable objectives while preserving chemical validity and diversity. The non-autoregressive nature of diffusion language model further enables iterative refinement of molecular fragments at inference time. Experiments on structure-conditioned, property-conditioned, and dual-conditioned benchmarks demonstrate consistent improvements over state-of-the-art methods in binding affinity, drug-likeness, and success rate, highlighting the effectiveness of our framework.

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