The weld pool and keyhole geometries are critical characteristics in evaluating the stability of the high-power laser beam welding (LBW) process and determining the resultant weld quality. However, obtaining these data through experimental or numerical methods remains challenging due to the difficulties in experimental measurements and the high computational demands of numerical modelling. This paper presents a physics-informed generative approach for predicting weld pool and keyhole geometries in the LBW process. With the help of a well experimentally validated numerical model considering the underlying physics in the LBW, including heat transfer, fluid flow, and keyhole dynamics, the geometries of the weld pool and keyhole under various welding conditions are calculated, serving as the dataset of the generative model. A conditional Variational Autoencoder (cVAE) model is employed to generate realistic 2D weld pool and keyhole geometries from the welding parameters. We utilize a β-VAE model with the Evidence Lower Bound (ELBO) loss function and include KL divergence annealing to better optimize model performance and stability during training. The generated results show a good agreement with the ground truth from the numerical simulation. The proposed approach exhibits the potential of physics-informed generative models for a rapid and accurate prediction of the weld pool geometries across a diverse range of process parameters, offering a computationally efficient alternative to full numerical simulations for process optimization and control in laser welding processes.