Molecular Denoising Using Diffusion Models with Physics-Informed Priors

Denoising Diffusion Probabilistic Models (DDPMs) are powerful generative models that have demonstrated superior performance in a variety of tasks and applications in material science and molecular graph modeling. Inspired by nonequilibrium statistical mechanics, these models iteratively degrade data through a forward diffusion process and then restore it by learning the time-reversal of the forward process. Despite their success, a significant drawback of DDPMs is their reliance on numerous iterations to generate high-quality samples, resulting in slow sampling. In this Letter, we introduce a strategy to improve DDPMs for atomistic systems by leveraging the thermodynamics of the data by deriving physics-informed priors. Drawing on principles from statistical mechanics, we derive physics-informed parameters for the prior distribution to initialize the Markov chain closer to the true data distribution. This strategy shortens the Markov chain, thereby improving the model's training efficiency and accelerating the sampling process. We demonstrate the effectiveness of our method in denoising noisy radial distribution functions obtained from a single atomic configuration of diverse Lennard-Jones and multiatomic liquids.