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This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential…

Machine Learning · Computer Science 2022-01-17 Victor Garcia Satorras , Emiel Hoogeboom , Fabian B. Fuchs , Ingmar Posner , Max Welling

The vast applications of deep generative models are anchored in three core capabilities -- generating new instances, reconstructing inputs, and learning compact representations -- across various data types, such as discrete text/protein…

Machine Learning · Computer Science 2024-06-06 Guangyi Liu , Yu Wang , Zeyu Feng , Qiyu Wu , Liping Tang , Yuan Gao , Zhen Li , Shuguang Cui , Julian McAuley , Zichao Yang , Eric P. Xing , Zhiting Hu

Denoising diffusion models have shown great potential in multiple research areas. Existing diffusion-based generative methods on de novo 3D molecule generation face two major challenges. Since majority heavy atoms in molecules allow…

Machine Learning · Computer Science 2024-04-23 Can Xu , Haosen Wang , Weigang Wang , Pengfei Zheng , Hongyang Chen

Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis. Flows can generate molecules effectively by inverting the encoding process, however, existing flow models either…

Machine Learning · Computer Science 2022-10-14 Yogesh Verma , Samuel Kaski , Markus Heinonen , Vikas Garg

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,…

Chemical Physics · Physics 2025-12-05 Peining Zhang , Jinbo Bi , Minghu Song

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation…

Machine Learning · Computer Science 2024-12-09 Sirui Xie , Zhisheng Xiao , Diederik P Kingma , Tingbo Hou , Ying Nian Wu , Kevin Patrick Murphy , Tim Salimans , Ben Poole , Ruiqi Gao

Cryo-EM reconstruction algorithms seek to determine a molecule's 3D density map from a series of noisy, unlabeled 2D projection images captured with an electron microscope. Although reconstruction algorithms typically model the 3D volume as…

Biomolecules · Quantitative Biology 2021-07-06 Ellen D. Zhong , Adam Lerer , Joseph H. Davis , Bonnie Berger

The Gaussian diffusion model, initially designed for image generation, has recently been adapted for 3D point cloud generation. However, these adaptations have not fully considered the intrinsic geometric characteristics of 3D shapes,…

Graphics · Computer Science 2024-08-01 Dengsheng Chen , Jie Hu , Xiaoming Wei , Enhua Wu

De novo 3D molecule generation is a pivotal task in drug discovery. However, many recent geometric generative models struggle to produce high-quality 3D structures, even if they maintain 2D validity and topological stability. To tackle this…

Machine Learning · Computer Science 2025-05-27 Danny Reidenbach , Filipp Nikitin , Olexandr Isayev , Saee Paliwal

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from.…

Machine Learning · Computer Science 2026-05-19 Christoph Griesbacher , Lea Bogensperger , Andreas Habring , Thomas Pock

Shape-based virtual screening is widely employed in ligand-based drug design to search chemical libraries for molecules with similar 3D shapes yet novel 2D chemical structures compared to known ligands. 3D deep generative models have the…

Chemical Physics · Physics 2022-10-12 Keir Adams , Connor W. Coley

Generative models of 3D molecular structure play a rapidly growing role in the design and simulation of molecules. Diffusion models currently dominate the space of 3D molecule generation, while autoregressive models have trailed behind. In…

Machine Learning · Computer Science 2025-09-10 Austin H. Cheng , Chong Sun , Alán Aspuru-Guzik

Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…

Computational Physics · Physics 2023-10-10 Zihan Zhou , Ruiying Liu , Chaolong Ying , Ruimao Zhang , Tianshu Yu

This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…

Machine Learning · Computer Science 2024-11-12 Oliver T. Unke , Hartmut Maennel

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have…

Computation and Language · Computer Science 2025-03-10 Minkai Xu , Tomas Geffner , Karsten Kreis , Weili Nie , Yilun Xu , Jure Leskovec , Stefano Ermon , Arash Vahdat

Extracting 3D atomic coordinates from spectroscopic data is a longstanding inverse problem. We present an equivariant diffusion model that generates site-specific 3D structures directly from near-edge spectra (ELNES/XANES). Trained on Si-O…

Materials Science · Physics 2026-02-19 Ren Okubo , Yu Fujikata , Izumi Takahara , Teruyasu Mizoguchi

Diffusion models have recently emerged as a powerful technique in image generation, especially for image super-resolution tasks. While 2D diffusion models significantly enhance the resolution of individual images, existing diffusion-based…

Computer Vision and Pattern Recognition · Computer Science 2024-11-27 Bohao Chen , Yanchao Zhang , Yanan Lv , Hua Han , Xi Chen

Diffusion models currently achieve state-of-the-art performance for both conditional and unconditional image generation. However, so far, image diffusion models do not support tasks required for 3D understanding, such as view-consistent 3D…

Computer Vision and Pattern Recognition · Computer Science 2024-02-22 Titas Anciukevičius , Zexiang Xu , Matthew Fisher , Paul Henderson , Hakan Bilen , Niloy J. Mitra , Paul Guerrero

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…

Machine Learning · Computer Science 2022-03-01 Bahar Azari , Deniz Erdoğmuş

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the…

Chemical Physics · Physics 2024-03-26 Yuxuan Song , Jingjing Gong , Yanru Qu , Hao Zhou , Mingyue Zheng , Jingjing Liu , Wei-Ying Ma