To improve the efficiency and flexibility of airfoil design, this paper proposes an airfoil generation method based on denoising diffusion probabilistic models (DDPM), named Airfoil-DDPM. This method does not rely on traditional parameterization methods. It uses a diffusion model to directly learn airfoil geometric features and generate airfoils. Thus, it avoids the limitation of preset parameter functions on shape diversity. By combining U-Net and an attention mechanism, the model accurately captures the geometric details of training samples. The generated airfoils have smooth surfaces and continuous curvature. Experimental results on the UIUC airfoil dataset show that the geometric error of the airfoils generated by Airfoil-DDPM is less than 5×10⁻³. When generating airfoils, the method not only reproduces the geometric features of NACA 0012 and RAE 2822 airfoils with high accuracy, but also meets their aerodynamic performance requirements. Principal component analysis visualization and target space analysis further show that the samples generated by Airfoil-DDPM cover the entire feature space of the UIUC dataset. They are also distributed over a wider range of lift and drag coefficients. This demonstrates its significant advantage in design diversity. This study provides an efficient and flexible parameterization-free solution for airfoil generation. It is helpful for promoting research on aircraft design and optimization.