A Periodic Bayesian Flow for Material Generation

2025-02-04

AI Summary

Crystal generation faces fundamental challenges in modeling non-Euclidean periodic structures, where existing methods struggle to simultaneously preserve lattice symmetries and capture complex distributional characteristics. To address this, we propose the Periodic Bayesian Flow (PBF) framework—a novel generative paradigm grounded in differential geometry and Bayesian inference. PBF introduces a non-monotonic entropy-driven dynamics, using entropy—not time—as the evolution parameter, thereby enabling the first rigorous extension of Bayesian flows to discrete periodic manifolds. It further incorporates crystallographic symmetry embeddings and manifold-aware probabilistic modeling to ensure physical consistency. Evaluated on benchmarks including MP-20, PBF establishes new state-of-the-art performance: it significantly improves both structure prediction accuracy and *de novo* generation quality, while reducing sampling steps from 2000 to just 10—a 100× speedup. PBF thus provides a differentiable, interpretable, and physically grounded foundation for crystal generation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Generative modeling of crystal data distribution is an important yet challenging task due to the unique periodic physical symmetry of crystals. Diffusion-based methods have shown early promise in modeling crystal distribution. More recently, Bayesian Flow Networks were introduced to aggregate noisy latent variables, resulting in a variance-reduced parameter space that has been shown to be advantageous for modeling Euclidean data distributions with structural constraints (Song et al., 2023). Inspired by this, we seek to unlock its potential for modeling variables located in non-Euclidean manifolds e.g. those within crystal structures, by overcoming challenging theoretical issues. We introduce CrysBFN, a novel crystal generation method by proposing a periodic Bayesian flow, which essentially differs from the original Gaussian-based BFN by exhibiting non-monotonic entropy dynamics. To successfully realize the concept of periodic Bayesian flow, CrysBFN integrates a new entropy conditioning mechanism and empirically demonstrates its significance compared to time-conditioning. Extensive experiments over both crystal ab initio generation and crystal structure prediction tasks demonstrate the superiority of CrysBFN, which consistently achieves new state-of-the-art on all benchmarks. Surprisingly, we found that CrysBFN enjoys a significant improvement in sampling efficiency, e.g., ~100x speedup 10 v.s. 2000 steps network forwards) compared with previous diffusion-based methods on MP-20 dataset. Code is available at https://github.com/wu-han-lin/CrysBFN.

Problem

• Generative modeling of crystal data
• Overcoming non-Euclidean manifold challenges
• Introducing CrysBFN for crystal generation

Innovation

• Periodic Bayesian Flow
• Non-monotonic entropy dynamics
• Entropy conditioning mechanism