  Using simulations or experiments performed at some set of temperatures to
learn about the physics or chemistry at some other arbitrary temperature is a
problem of immense practical and theoretical relevance. Here we develop a
framework based on statistical mechanics and generative Artificial Intelligence
that allows solving this problem. Specifically, we work with denoising
diffusion probabilistic models, and show how these models in combination with
replica exchange molecular dynamics achieve superior sampling of the
biomolecular energy landscape at temperatures that were never even simulated
without assuming any particular slow degrees of freedom. The key idea is to
treat the temperature as a fluctuating random variable and not a control
parameter as is usually done. This allows us to directly sample from the joint
probability distribution in configuration and temperature space. The results
here are demonstrated for a chirally symmetric peptide and single-strand
ribonucleic acid undergoing conformational transitions in all-atom water. We
demonstrate how we can discover transition states and metastable states that
were previously unseen at the temperature of interest, and even bypass the need
to perform further simulations for wide range of temperatures. At the same
time, any unphysical states are easily identifiable through very low Boltzmann
weights. The procedure while shown here for a class of molecular simulations
should be more generally applicable to mixing information across simulations
and experiments with varying control parameters.
