Introduction: Join Linköping University, a vibrant community of over 40,000 students and employees dedicated to tackling contemporary challenges with credibility, trust, and safety. We encourage boldness, free thinking, and innovation to create a better future together. Responsibilities: We seek a PhD candidate to work at the intersection of computational statistics and machine learning, focusing on methods based on differential equations. The research will be fundamental, aiming to develop computationally efficient and statistically principled new models and methods for modern machine learning problems. Key tasks include developing new models and methods for generative sampling and Bayesian inference, especially involving generative diffusion models with applications in image and material generation, scientific computing, and Bayesian inverse problems. Qualifications: Applicants must hold a master's degree or equivalent in applied mathematics, statistics, machine learning, control theory, computer science, or a related field relevant to the project's research problems. Excellent English skills (spoken and written), strong collaboration and communication abilities are required. Experience in stochastic (partial) differential equations, generative diffusion and flow models, Bayesian inference, sequential Monte Carlo, Markov chain Monte Carlo, and inverse problems are highly meritorious. Strong academic results, a solid background in mathematics and statistics, and strong motivation for theoretical and methodological research are also preferred. Programming skills in Python are mandatory, with experience in JAX or Julia considered a plus.