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

Diffusion models have emerged as the state-of-the-art method in generative artificial intelligence (AI) and have shown great success in image synthesis, video generation, molecular design, and protein structure prediction. For biophysical problems, such as protein folding and association, a fundamental question in diffusion-based methods is how their learned functions correspond to thermodynamics. In this paper, we study diffusion models through the lens of theoretical biophysics, analyzing their underlying formulation of potentials and exploring their applications in scoring protein interactions. We develop simple theories rooted in statistical physics that relate thermodynamic potentials to the negative log of the probability of observing a system in a particular state. We include dimensional analysis of diffusion model equations and a table mapping AI and physics jargon. We then test a diffusion models ability to capture learned energies as negative log-likelihood values, - log p0(x0), by integrating over the diffusion-generated path or a probability flow path. We test these integrals on a simple 1D Gaussian mixture diffusion model and a protein-docking diffusion model, DFMDock. In the 1D case, we find that integration over both diffusion and flow paths can accurately recover ground truth probabilities. When we extract the learned docking energies for cases where DFMDock succeeds, we observe energy funnels with the minimum energy near the experimental docked structure, like those we observe with Rosetta, an empirically tuned physics-based biomolecular modeling suite. The learned energy performs comparably or outperforms Rosetta interface energy in 6 out of 25 cases at ranking the correctness of docked poses. These data show that we can extract a relevant learned energy function from a diffusion model and compare it to physical energy functions.