Can We Extract Physics-like Energies from Generative Protein Diffusion Models?

Area of Science:

• Theoretical Biophysics
• Computational Biology
• Generative Artificial Intelligence (AI)

Background:

• Diffusion models are state-of-the-art in AI, excelling in image, video, and molecular design.
• A key question is how diffusion models' learned functions relate to thermodynamics in biophysical systems.
• Understanding this connection is vital for applications like protein folding and association.

Purpose of the Study:

• To analyze diffusion models through the lens of theoretical biophysics.
• To investigate the relationship between thermodynamic potentials and diffusion model formulations.
• To explore the application of diffusion models in scoring protein interactions.

Main Methods:

• Developed theories from statistical physics linking thermodynamic potentials to negative log-likelihood.
• Performed dimensional analysis of diffusion model equations.
• Tested diffusion models on 1D Gaussian mixture and protein-docking (DFMDock) tasks, integrating over diffusion and probability flow paths.

Main Results:

• Accurate recovery of ground truth probabilities in the 1D case using integrated paths.
• DFMDock exhibited energy funnels with minima near experimental structures for successful predictions.
• Learned energies from DFMDock comparably or outperformed Rosetta in ranking docked poses in 6/25 cases.

Conclusions:

• Diffusion models can capture and represent learned energy functions relevant to biophysical systems.
• Extracted energy functions from diffusion models can be compared to traditional physics-based energy functions.
• This work bridges generative AI and theoretical biophysics for molecular modeling and design.