Abstract: In this talk, I will introduce a flow-based nonperturbative method to study the first-order phase transition (FOPT) of a scalar field theory on a lattice. Motivated by possible early-universe first-order electroweak and QCD phase transitions and recent developments in machine learning tools, including normalizing flows (NFs) for lattice field theory, we have developed a simulation algorithm to efficiently calculate bubble nucleation rates. We propose the ``partitioning flow-based (PF) sampling" method to overcome two challenges in the application of NFs for lattice field theory: the "mode-collapse" and "rare-event sampling" problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the capability of our PF method to calculate the nucleation rates for the thermal FOPT. This method could be applied to (3+1)-dimensional theories and used to study realistic cosmological phase transitions.