The primary objective of general-purpose detectors at the Large Hadron Collider (LHC) is to identify new physics beyond the Standard Model (SM). A critical component of these analyses involves simulating data for comparison with real detector outputs. The demand for simulated data escalates proportionally with the accumulation of real data, and the associated computational costs are substantial. Consequently, the development of efficient generative methods is essential.

This thesis introduces two innovative score-based generative models utilizing transformers for the rapid generation of jets represented as point clouds. These models, termed PC-JeDi and PC-Droid, are capable of conditionally generating jets from various sources while achieving high fidelity in their kinematic properties. Comparative analyses demonstrate that both models surpass existing state-of-the-art generative models in terms of speed and quality of generation.

Given the vast landscape of potential new physics, direct individual searches are impractical. An effective alternative is to investigate deviations from SM predictions in a model independent framework. This thesis proposes four novel model-independent search techniques for new physics at the LHC. Each method is based on generating a background enriched template within a specified region of interest, which is then compared to observed data to assess the presence of new physics. The methods differ in their template generation approaches, training durations, and applicability scopes. All methods are employed to explore new physics in the dijet invariant mass spectrum, with results benchmarked against contemporary state-of-the-art search methodologies whenever feasible. Given the generic nature of the proposed methods, they can be readily adapted to other search channels both in the context of High Energy Physics and beyond.