Understanding transition paths between meta-stable states in molecular systems is fundamental for material design and drug discovery. However, sampling these paths using molecular dynamics simulation is computationally prohibitive due to the high-energy barriers between the meta-stable states. Recent machine learning approaches, although promising, are mostly restricted to simple systems or rely on collective variables (CVs) extracted from expensive domain knowledge. In this work, we propose to leverage generative flow networks (GFlowNets) for sampling transition paths without relying on CVs. We train a bias potential parameterized by a neural network, based on reformulating the problem as amortized energy-based sampling over molecular trajectories. The training objective is to minimize the squared log ratio between the target distribution and the sampler, derived from the flow matching objective. Our evaluation on four proteins (Alanine Dipeptide, Histidine Dipeptide, Polyproline, and Chignolin) demonstrates the superiority of our work compared to the previous CV-free machine learning approach for discovering realistic and diverse transition paths.