Porous materials such as zeolites and Metal-Organic Frameworks are widely used for molecular separations based on adsorption and enthalpy/entropy characteristics. Ideal adsorption solution theory (IAST) predicts mixture adsorption behaviour on the basis of pure component isotherms of adsorbents in porous media. Mixture data at all mole fractions are required for breakthrough simulations. The use of IAST avoids the expensive computations of mixtures with Monte Carlo methods. Matching outcomes from computational physics studies to experimentally measurable properties is the foundation of the materials design pipeline. Here, we report the regression of an Invertible Autoencoder (IAE) for the forward and backward mapping of pure and mixture isotherms. The invertible autoencoder is defined as a soft-invertible neural network, which can be used as mapping function. Pure component isotherms are modelled using a 3-site Langmuir-Freundlich model, with a broad range of equilibrium pressure and heterogeneity factors. A synthetic dataset is generated from pure component isotherms and mixture isotherms calculated with RUPTURA. The IAE predicts pure and mixture isotherms with high precision over a large fugacity range, for up to 6 components and 3-site isotherms. This work contributes to inverting the full design pipeline from physical gas separation to adsorbate design, enabling property-guided materials discovery.