Latent thermodynamic flows: unified representation learning and generative modeling of temperature-dependent behaviors from limited data

, collective variables, classify metastable states, and generate equilibrium distributions across temperatures beyond the training data. The joint optimization of representation learning and generative modeling allows LaTF to mutually enhance both components, making optimal use of costly simulation data to accurately reproduce the system's equilibrium behaviors over the meaningful latent representation that captures its slow, essential degrees of freedom. We demonstrate LaTF's effectiveness across diverse systems, including a model potential, the Chignolin protein, and a cluster of Lennard-Jones particles, with thorough evaluations and benchmarking using multiple metrics and extensive simulations. Moreover, we apply LaTF to a RNA tetraloop system, where despite using simulation data from only two temperatures, LaTF reconstructs the temperature-dependent structural ensemble and melting behavior, consistent with experimental and prior extensive computational results.