The Standard Model of particle physics is the most successful theory describing the fundamental properties of matter that govern the universe. At the Large Hadron Collider at CERN, these properties are studied by colliding high energetic particles together, which has led to significant discoveries, including the Higgs boson in 2012. Due to the complexity of these collisions, advanced Machine Learning techniques have recently been employed to improve reconstruction and simulation performance. The reconstruction methods are often derived from simulations that attempt to model the underlying physics processes. However, due to mismodelling in simulations, advanced calibration or domain-shift adaptation techniques are required to ensure accurate reconstruction. This thesis will consider proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider, and present a method that leverages Optimal Transport to derive a fully continuous calibration that transforms the simulated data to observed data with minimal squared Euclidean distance. The method will derive a b-jet calibration in the t ¯t region of the DL1r heavy-flavour tagger deployed at the ATLAS experiment. Comparisons made between the existing DL1r b-jet calibration and the Optimal Transport-based calibration show comparable results. The additional benefit of the Optimal Transport-based calibration is its fully continuous and high-dimensional nature, that allows all selections and discriminants to be calibrated simultaneously. This is tested using the VH, H → cc tagging categories. On a toy collision dataset, the Optimal Transport-based calibration is extended to a highdimensional latent representation of a jet tagger, showing the scalability of the method and enabling high-dimensional calibrated representations to be utilized for other reconstruction tasks or allowing more jet information to be utilized by physics analyses. The same Optimal Transport-based method is also extended to decorrelate representations from protected attributes such as invariant mass. This is demonstrated on a multi-class large-radius jet tagger, where the method is shown to reduce mass sculpting while retaining good classification performance compared to existing methods. Additionally, an approach to perform pileup mitigation on large-radius jet using diffusion models is presented. Traditional methods use a classification-style scheme to identify and remove pileup contributions, however, due to reconstruction inefficiencies not all constituents from the hard-scatter are reconstructed. This generative approach is both able to account reconstruction inefficiencies and generate a PU-free jet which will be crucial for HighLuminosity Large Hadron Collider