Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation

Junyi An; Chao Qu; Yun-Fei Shi; Zhijian Zhou; Fenglei Cao; Yuan Qi

cs.LGMar 10, 2026

Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation

Authors: Junyi An, Chao Qu, Yun-Fei Shi, Zhijian Zhou, Fenglei Cao, Yuan Qi

Organizations: Shanghai Academy of Artificial Intelligence for Science, SAIS · Artificial Intelligence Innovation and Incubation (AI3) Institute, Fudan University

Abstract

Recent 3D molecular generation methods primarily use asynchronous auto-regressive or synchronous diffusion models. While auto-regressive models build molecules sequentially, they're limited by a short horizon and a discrepancy between training and inference. Conversely, synchronous diffusion models denoise all atoms at once, offering a molecule-level horizon but failing to capture the causal relationships inherent in hierarchical molecular structures. We introduce Equivariant Asynchronous Diffusion (EAD) to overcome these limitations. EAD is a novel diffusion model that combines the strengths of both approaches: it uses an asynchronous denoising schedule to better capture molecular hierarchy while maintaining a molecule-level horizon. Since these relationships are often complex, we propose a dynamic scheduling mechanism to adaptively determine the denoising timestep. Experimental results show that EAD achieves state-of-the-art performance in 3D molecular generation.

Figures & tables

Figure 1: Generation Processes Overview. Left: Autoregressive methods generate atoms sequentially, with each new atom’s generation conditioned on the previously generated, noise-free atoms. Middle: Full-molecule diffusion models denoise all atoms simultaneously, iteratively refining a sample of noisy atoms until they are all noise-free. Right: Our proposed EAD model combines the strengths of both approaches by using an asynchronous denoising process. This allows atoms to become noise-free sequentially, where the denoising direction for each atom can benefit from the information of atoms that have already reached a lower noise state. Details of their difference can be found in Section 3.2 .

Figure 2

Model	Atom sta(%)	Mol sta(%)	Valid(%)	V*U(%)	Sec./sample
E-NF	85.0	4.9	40.2	39.4	-
G-Schnet	95.7	68.1	85.5	80.3	-
EDM	98.7 $\pm 0.1\%$	82.0 $\pm 0.4\%$	91.9 $\pm 0.5\%$	90.7 $\pm 0.6\%$	0.20
GDM	97.6	71.6	90.4	89.5	-
EDM-Bridge	98.8	84.6	92.0	90.7	-
GeoLDM	98.9	89.4	93.8	92.7	-

Table 1: Comparison of generation performance on the QM9 dataset, including atom stability, molecule stability, validity, and validity*uniqueness. Higher values indicate better performance. Gray shading denotes the base model used for EAD.

Metrics	EDM	GDM	EDM-Bridge	GeoLDM	UniGEM	EAD (Ours)
Atom sta(%)	81.3	77.7	82.4	84.4	85.1	86.3
Valid(%)	92.6	91.8	92.8	99.3	98.4	99.1

Table 2: Comparison of generation performance on GEOM-DRUG dataset.

Task	$\alpha$	$\Delta\varepsilon$	$\varepsilon_{\mathrm{HOMO}}$	$\varepsilon_{\mathrm{LUMO}}$	$\mu$	$C_{v}$
Units	Bohr 3	meV	meV	meV	D	$\frac{\text{cal}}{\text{mol}}$ K
#Atoms	3.86	866	426	813	1.053	1.971
EDM	2.76	655	356	584	1.111	1.101
GeoLDM	2.37	587	340	522	1.108	1.025
EAD	2.24	564	318	516	0.999	0.945
QM9 (L-bound)	0.10	64	39	36	0.043	0.040

Table 3: Mean Absolute Error for molecular property prediction by a EGNN classifier

\phi_{c}

on a QM9 subset.

Sampling strategy	Atom sta(%)	Mol sta(%)	Valid(%)	V*U(%)
Synchronous schedule	98.7	81.9	91.9	90.2
Manual asynchronous schedule	90.5	64.0	87.2	81.7
Adaptive asynchronous schedule	99.0	90.3	95.1	93.2

Table 4: Comparison of different sampling strategies.

Configuration	Mol sta(%)	Valid(%)	Configuration	Mol sta(%)	Valid(%)
$\lambda=0.8,w=2$	90.3	95.1	$\lambda=0.9,w=2$	89.1	94.0
$\lambda=0.8,w=1$	90.0	94.8	$\lambda=0.6,w=2$	64.7	79.5
$\lambda=0.8,w=5$	80.4	90.5	$\lambda=0.4,w=2$	12.5	36.4
$\lambda=0.8,w=10$	60.2	77.8	$\lambda=0.2,w=2$	0.5	20.8

Table 5: Comparison of different hyper-parameter configuration. Gray grid denotes the default configuration.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Molecular Size	EDM Uniqueness (%) $\uparrow$	EAD Uniqueness (%) $\uparrow$
30 (0 molecules in the training set)	35.68	44.33
29 (25 molecules)	45.09	60.18
28 (0 molecules)	45.61	65.40

Appendix

Table 6: Uniqueness and novelty over 10000 molecules with defined molecular size.

Figure 2: Extra samples generated by EAD trained on the QM9 dataset.

Explore similar work

VEDA: Generation of 3D Molecules via Variance-Exploding Diffusion with Annealing
Nov 11, 2025Peining Zhang, Jinbo Bi, Minghu Song3D Molecular Generation Diffusion Models
University of Connecticut, Storrs, Connecticut 06269, USA · Institute of Health and Medicine, Hefei Comprehensive National Science Center, Hefei 230601, China
Autoregressive latent diffusion for 3D molecule generation
Jul 10, 2026Federico Ottomano, Gaopeng Ren, Yingzhen Li +2Latent Diffusion Models Molecular Graph Generation
Department of Chemistry Imperial College London · Department of Computing Imperial College London
Fine-Tuning Diffusion Models for Molecular Generation via Reinforcement Learning and Fast Sampling
May 31, 2026Guang Lin, Shikui Tu, Lei XuMolecular Optimization Diffusion Model Fine-Tuning
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, Guangdong, China

Nov 11, 2025J/K move · Enter open · S save

VEDA: Generation of 3D Molecules via Variance-Exploding Diffusion with Annealing

Peining Zhang, Jinbo Bi, Minghu Song

University of Connecticut, Storrs, Connecticut 06269, USA · Institute of Health and Medicine, Hefei Comprehensive National Science Center, Hefei 230601, China

3D Molecular Generation Diffusion Models Diffusion Sampling Equivariant Neural Networks

Open paper AskPDF arXiv

Diffusion models show promise for 3D molecular generation, but face a fundamental trade-off between sampling efficiency and conformational accuracy. While flow-based models are fast, they often produce geometrically inaccurate structures, as they have difficulty capturing the multimodal distributions of molecular conformations. In contrast, denoising diffusion models are more accurate but suffer from slow sampling, a limitation attributed to sub-optimal integration between diffusion dynamics and SE(3)-equivariant architectures. To address this, we propose VEDA, a unified SE(3)-equivariant framework that combines variance-exploding diffusion with annealing to efficiently generate conformationally accurate 3D molecular structures. Specifically, our key technical contributions include: (1) a VE schedule that enables noise injection functionally analogous to simulated annealing, improving 3D accuracy and reducing relaxation energy; (2) a novel preconditioning scheme that reconciles the coordinate-predicting nature of SE(3)-equivariant networks with a residual-based diffusion objective, and (3) a new arcsin-based scheduler that concentrates sampling in critical intervals of the logarithmic signal-to-noise ratio. On the QM9 and GEOM-DRUGS datasets, VEDA matches the sampling efficiency of flow-based models, achieving state-of-the-art valency stability and validity with only 100 sampling steps. More importantly, VEDA's generated structures are remarkably stable, as measured by their relaxation energy during GFN2-xTB optimization. The median energy change is only 1.72 kcal/mol, significantly lower than the 32.3 kcal/mol from its architectural baseline, SemlaFlow. Our framework demonstrates that principled integration of VE diffusion with SE(3)-equivariant architectures can achieve both high chemical accuracy and computational efficiency.

Abstract

Explore similar work

VEDA: Generation of 3D Molecules via Variance-Exploding Diffusion with Annealing

Autoregressive latent diffusion for 3D molecule generation

Fine-Tuning Diffusion Models for Molecular Generation via Reinforcement Learning and Fast Sampling