Systematic Evolution of Ligands by Exponential Enrichment (SELEX)is a powerful method for discovering novel ligands with high affinity andspecificity for target molecules. However, the experimental process is timeconsuming,resource-intensive, and involves numerous parameters that cansignificantly impact the outcome. This thesis aims to develop an in-silico SELEXsimulator using advanced generative modeling approaches such as flow matchingand hidden Markovmodels. These powerful probabilistic frameworks can capturethe complex evolutionary dynamics of the SELEX process, enabling us to modelthe selection, binding, and amplification stages with high fidelity. By leveragingthese generative modeling techniques, we can streamline ligand discovery andoptimize experimental conditions through computational exploration.