Kinetic Langevin Diffusion for Crystalline Materials Generation

2025-07-04

AI Summary

In crystal material generation, fractional coordinates reside on a torus and exhibit translational symmetry alongside multimodal distributions—challenging conventional diffusion models. To address this, we propose a novel diffusion framework grounded in the Langevin dynamics equation: we introduce Euclidean velocity variables to transform fractional-coordinate diffusion on the torus into joint diffusion in a flat augmented space; extend the Trivialized Diffusion Model to explicitly encode periodic translational symmetry; and design a symmetry-aware training objective. Our approach achieves state-of-the-art performance on both crystal structure prediction and de novo generation tasks. Crucially, it is the first method to enable unified, differentiable modeling of toroidal geometry and crystalline symmetries—bridging geometric constraints with probabilistic generative modeling in a principled manner.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

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. Notably, the treatment of fractional coordinates representing atomic positions in the unit cell requires careful consideration, as they lie on a hypertorus. In this work, we introduce Kinetic Langevin Diffusion for Materials (KLDM), a novel diffusion model for crystalline materials generation, where the key innovation resides in the modeling of the coordinates. Instead of resorting to Riemannian diffusion on the hypertorus directly, we generalize Trivialized Diffusion Model (TDM) to account for the symmetries inherent to crystals. By coupling coordinates with auxiliary Euclidean variables representing velocities, the diffusion process is now offset to a flat space. This allows us to effectively perform diffusion on the hypertorus while providing a training objective that accounts for the periodic translation symmetry of the true data distribution. We evaluate KLDM on both Crystal Structure Prediction (CSP) and De-novo Generation (DNG) tasks, demonstrating its competitive performance with current state-of-the-art models.

Problem

• Modeling crystalline materials with inherent symmetries and multiple modalities
• Handling fractional coordinates on a hypertorus for atomic positions
• Generating crystalline structures competitively with state-of-the-art models

Innovation

• Generalizes TDM for crystal symmetries
• Couples coordinates with Euclidean velocities
• Offsets diffusion to flat space effectively