Invertible neural networks are a recent technique in machine learning promising neural network architectures that can be run in forward and reverse mode. In this paper, we will be introducing invertible surrogate models that approximate complex forward simulation of the physics involved in laser plasma accelerators: iLWFA. The bijective design of the surrogate model also provides all means for reconstruction of experimentally acquired diagnostics. The quality of our invertible laser wakefield acceleration network will be verified on a large set of numerical LWFA simulations.