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Radynversion infers solar atmospheric properties during a solar flare. The code is based on an Invertible Neural Network (INN) that is trained to learn an approximate bijective mapping between the atmospheric properties of electron density, temperature, and bulk velocity (all as a function of altitude), and the observed Hα and Ca II λ8542 line profiles. As information is lost in the forward process of radiation transfer, this information is injected back into the model during the inverse process by means of a latent space; the training allows this latent space to be filled using an n-dimensional unit Gaussian distribution, where n is the dimensionality of the latent space. The code is based on a model trained by simulations made by RADYN, a 1D non-equilibrium radiation hydrodynamic model with good optically thick radiation treatment that does not consider magnetic effects.