Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. We propose a new class of algorithms for clustering jets that use infrared and collinear safe mixture models. These new algorithms, known as fuzzy jets, are clustered using maximum likelihood techniques and can dynamically determine various properties of jets like their size. We show that the fuzzy jet size adds additional information to conventional jet tagging variables in boosted topologies. Furthermore, we study the impact of pileup and show that with some slight modifications to the algorithm, fuzzy jets can be stable up to high pileup interaction multiplicities.