Related papers: Clifford Group Equivariant Diffusion Models for 3D…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…

The bifurcation of generative modeling into autoregressive approaches for discrete data (text) and diffusion approaches for continuous data (images) hinders the development of truly unified multimodal systems. While Masked Language Models…

Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an…

Diffusion-based generative models represent the current state-of-the-art for image generation. However, standard diffusion models are based on Euclidean geometry and do not translate directly to manifold-valued data. In this work, we…

Probabilistic denoising diffusion models (DDMs) have set a new standard for 2D image generation. Extending DDMs for 3D content creation is an active field of research. Here, we propose TetraDiffusion, a diffusion model that operates on a…

We introduce Equivariant Neural Diffusion (END), a novel diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Compared to current state-of-the-art equivariant diffusion models, the key innovation…

3D molecule generation is crucial for drug discovery and material science, requiring models to process complex multi-modalities, including atom types, chemical bonds, and 3D coordinates. A key challenge is integrating these modalities of…

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…

Molecular conformation generation plays key roles in computational drug design. Recently developed deep learning methods, particularly diffusion models have reached competitive performance over traditional cheminformatical approaches.…

Generative modeling of crystalline materials using diffusion models presents a series of challenges: the data distribution is characterized by inherent symmetries and involves multiple modalities, with some defined on specific manifolds.…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

Understanding and representing the structure of 3D objects in an unsupervised manner remains a core challenge in computer vision and graphics. Most existing unsupervised keypoint methods are not designed for unconditional generative…

Diffusion models have shown great promise for image generation, beating GANs in terms of generation diversity, with comparable image quality. However, their application to 3D shapes has been limited to point or voxel representations that…

Generative AI presents chemists with novel ideas for drug design and facilitates the exploration of vast chemical spaces. Diffusion models (DMs), an emerging tool, have recently attracted great attention in drug R\&D. This paper…

Generative models have the potential to accelerate key steps in the discovery of novel molecular therapeutics and materials. Diffusion models have recently emerged as a powerful approach, excelling at unconditional sample generation and,…

Diffusion models have emerged as powerful tools for molecular generation, particularly in the context of 3D molecular structures. Inspired by non-equilibrium statistical physics, these models can generate 3D molecular structures with…

Inspired by Geoffrey Hinton emphasis on generative modeling, To recognize shapes, first learn to generate them, we explore the use of 3D diffusion models for object classification. Leveraging the density estimates from these models, our…

This paper explains how, following the representation of 3D crystallographic space groups in Clifford's geometric algebra, it is further possible to similarly represent the 162 so called subperiodic groups of crystallography in Clifford's…

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion…