ProT-GFDM: A Generative Fractional Diffusion Model for Protein Generation

Abstract: This work introduces the generative fractional diffusion model for protein generation (ProT-GFDM), a novel generative framework that employs fractional stochastic dynamics for protein backbone structure modeling. This approach builds on the continuous-time score-based generative diffusion modeling paradigm, where data are progressively transformed into noise via a stochastic differential equation and reversed to generate structured samples. Unlike classical methods that rely on standard Brownian motion, ProT-GFDM employs a fractional stochastic process with superdiffusive properties to improve the capture of long-range dependencies in protein structures. Trained on protein fragments from the Protein Data Bank, ProT-GFDM outperforms conventional score-based models, achieving a 7.19% increase in density, a 5.66% improvement in coverage, and a 1.01% reduction in the Frechet inception distance. By integrating fractional dynamics with computationally efficient sampling, the proposed framework advances generative modeling for structured biological data, with implications for protein design and computational drug discovery.