Probability density function (pdf) estimation is a long-standing and fundamental problem in statistics. Most tasks in machine learning, including classification and regression, become much easier with a good density estimate. Pdf estimation aims to characterise the continuous distribution underlying a random set of samples. Here at BIG and CIBM there is an ongoing effort to find the best technique to this end. Applications include positron emission tomography (PET) imaging and scanning transmission x-ray microscopy (STXM). In this project, we will explore the limits of advanced machine learning techniques (e.g., complex deep-neural-network architectures such as real NVP or spline interpolations) for pdf estimation. We will focus on understanding the fundamentals behind these methods and assess their advantages and limitations for different applications. The student should be comfortable with probability and statistics and familiar with the PyTorch framework. Prior experience with signal processing or machine learning research is a definite plus.