This paper focuses on the topology optimization of a broadband acoustic transition section that connects two cylindricalwaveguides with different radii. The primary objective is to design a transition section that maximizes the transmission of aplanar acoustic wave while ensuring that the transmitted wave exhibits a planar shape. Helmholtz equation is used to modellinear wave propagation in the device. We utilize the finite element method to solve the state equation on a structured meshof square elements. Subsequently, a material distribution topology optimization problem is formulated to optimize the dis-tribution of sound-hard material in the transition section. We employ two different gradient-based approaches to solve theoptimization problem: namely, a deterministic approach using the method of moving asymptotes (MMA), and a stochasticapproach utilizing both stochastic gradient (SG) and continuous stochastic gradient (CSG) methods. A comparative analysisis provided among these methodologies concerning the design feasibility and the transmission performance of the optimizeddesigns, and the computational efficiency. The outcomes highlight the effectiveness of stochastic techniques in achievingenhanced broadband acoustic performance with reduced computational demands and improved design practicality. Theinsights from this investigation demonstrate the potential of stochastic approaches in acoustic applications, especially whenbroadband acoustic performance is desired.