Quotient-Space Diffusion Models

• URL: http://arxiv.org/abs/2604.21809v1
• Date: Thu, 23 Apr 2026 16:04:40 GMT
• Title: Quotient-Space Diffusion Models
• Abstract summary: We establish a formal framework for diffusion modeling on a general quotient space.<n>We apply it to molecular structure generation which follows the special Euclidean group $textSE(3)$ symmetry.<n>The arguments are empirically validated on structure generation for small molecules and proteins.
• Score: 30.277808058897104
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion-based generative models have reformed generative AI, and have enabled new capabilities in the science domain, for example, generating 3D structures of molecules. Due to the intrinsic problem structure of certain tasks, there is often a symmetry in the system, which identifies objects that can be converted by a group action as equivalent, hence the target distribution is essentially defined on the quotient space with respect to the group. In this work, we establish a formal framework for diffusion modeling on a general quotient space, and apply it to molecular structure generation which follows the special Euclidean group $\text{SE}(3)$ symmetry. The framework reduces the necessity of learning the component corresponding to the group action, hence simplifies learning difficulty over conventional group-equivariant diffusion models, and the sampler guarantees recovering the target distribution, while heuristic alignment strategies lack proper samplers. The arguments are empirically validated on structure generation for small molecules and proteins, indicating that the principled quotient-space diffusion model provides a new framework that outperforms previous symmetry treatments.

Related papers

• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction [54.95522167029998]
  This article is a self-contained primer on diffusion over general state spaces.<n>We develop the discrete-time view (forward noising via Markov kernels and learned reverse dynamics) alongside its continuous-time limits.<n>A common variational treatment yields the ELBO that underpins standard training losses.
  arXiv  Detail & Related papers  (2025-12-04T18:55:36Z)
• Energy-Based Flow Matching for Generating 3D Molecular Structure [7.055961224018033]
  We focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models.<n>Our view results in a mapping function, that is directly learned to textititeratively map random configurations.<n>Experiments on protein docking and protein backbone generation consistently demonstrate the method's effectiveness.
  arXiv  Detail & Related papers  (2025-08-26T11:42:57Z)
• UniGenX: a unified generative foundation model that couples sequence, structure and function to accelerate scientific design across proteins, molecules and materials [62.72989417755985]
  We present UniGenX, a unified generative model for function in natural systems.<n>UniGenX represents heterogeneous inputs as a mixed stream of symbolic and numeric tokens.<n>It achieves state-of-the-art or competitive performance for the function-aware generation across domains.
  arXiv  Detail & Related papers  (2025-03-09T16:43:07Z)
• Structure Language Models for Protein Conformation Generation [66.42864253026053]
  Traditional physics-based simulation methods often struggle with sampling equilibrium conformations.<n>Deep generative models have shown promise in generating protein conformations as a more efficient alternative.<n>We introduce Structure Language Modeling as a novel framework for efficient protein conformation generation.
  arXiv  Detail & Related papers  (2024-10-24T03:38:51Z)
• AUTODIFF: Autoregressive Diffusion Modeling for Structure-based Drug Design [16.946648071157618]
  We propose a diffusion-based fragment-wise autoregressive generation model for structure-based drug design (SBDD) We design a novel molecule assembly strategy named conformal motif that preserves the conformation of local structures of molecules first. We then encode the interaction of the protein-ligand complex with an SE(3)-equivariant convolutional network and generate molecules motif-by-motif with diffusion modeling.
  arXiv  Detail & Related papers  (2024-04-02T14:44:02Z)
• DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization [49.85944390503957]
  DecompOpt is a structure-based molecular optimization method based on a controllable and diffusion model. We show that DecompOpt can efficiently generate molecules with improved properties than strong de novo baselines.
  arXiv  Detail & Related papers  (2024-03-07T02:53:40Z)
• Diffusion-Driven Generative Framework for Molecular Conformation Prediction [0.66567375919026]
  The rapid advancement of machine learning has revolutionized the precision of predictive modeling in this context. This research introduces a cutting-edge generative framework named method. Method views atoms as discrete entities and excels in guiding the reversal of diffusion.
  arXiv  Detail & Related papers  (2023-12-22T11:49:39Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning [60.02391969049972]
  We introduce a novel deep learning framework, called Distributional Graphormer (DiG), in an attempt to predict the equilibrium distribution of molecular systems. DiG employs deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on a descriptor of a molecular system.
  arXiv  Detail & Related papers  (2023-06-08T17:12:08Z)
• EigenFold: Generative Protein Structure Prediction with Diffusion Models [10.24107243529341]
  EigenFold is a diffusion generative modeling framework for sampling a distribution of structures from a given protein sequence. On recent CAMEO targets, EigenFold achieves a median TMScore of 0.84, while providing a more comprehensive picture of model uncertainty.
  arXiv  Detail & Related papers  (2023-04-05T02:46:13Z)
• Structure-preserving GANs [6.438897276587413]
  We introduce structure-preserving GANs as a data-efficient framework for learning distributions. We show that we can reduce the discriminator space to its projection on the invariant discriminator space. We contextualize our framework by building symmetry-preserving GANs for distributions with intrinsic group symmetry.
  arXiv  Detail & Related papers  (2022-02-02T16:40:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.