Charge order is universal among high-T_c cuprates, but its relation to superconductivity is unclear. While static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. Using time-resolved resonant soft x-ray scattering at a free-electron laser, we show that the charge order in prototypical La_2−xBa_xCuO₄ exhibits transverse fluctuations at picosecond time scales. These sub–millielectron volt excitations propagate by Brownian-like diffusion and have an energy scale remarkably close to the superconducting T_c. At sub–millielectron volt energy scales, the dynamics are governed by universal scaling laws defined by the propagation of topological defects. Our results show that charge order in La_2−xBa_xCuO₄ exhibits dynamics favorable to the in-plane superconducting tunneling and establish time-resolved x-rays as a means to study excitations at energy scales inaccessible to conventional scattering techniques.