The paper addresses simulating laser wakefield electron acceleration experiments by using a novel training methodology for probabilistic diffusion models with adherence to the foundational physical principles. The methodology allows overcoming the inability of the common generative machine learning models to capture external data manifold constraints due to the nature of training. Laser wakefield electron acceleration is a highly complex non-linear phenomenon with a developed approximation theory, which, however, falls short in many extreme cases. Applying a model trained with physical constraint loss to simulate these experiments demonstrates strong performance and produces results that are positively evaluated by experts in the field. Moreover, due to the embedded physical information, it can extrapolate outside the range of training input data, based on the known physics of the process. This approach shows immense potential for using generative models in the modeling of complex scientific experiments, which helps in efficient experiment planning and optimization. We evaluate the generative models using Wasserstein distance calculated between distributions of charge of electrons at corresponding energies. This metric provides a robust quantification of the similarity between the predicted and reference electron energy spectra.