Mathematical Data Science Seminar Series

Monday, March 2, 2:30-3:30 p.m.

Extending Measure Dynamics Beyond Generative Modeling – Jiequn Han

Transport-based models, such as score-based diffusion and flow-matching models, have become a leading paradigm for generative modeling: from a dataset of samples, one learns dynamics that generate new samples from the same distribution. In many scientific settings, however, the objective is not simply to reproduce a training distribution, but to adapt or infer distributions under new constraints or incomplete observations. This motivates extending the transport viewpoint beyond the standard training-and-sampling setting.

I will describe two such directions. First, inference-time adaptation: modifying the inference dynamics induced by a pre-trained model to sample from new target distributions without retraining, while preserving stability and efficiency. Second, distributional inference from limited or noisy data: constructing measure dynamics that recover target distributions when the observation process is available only through a black-box simulator. Together, these examples illustrate how transport-based methods enable flexible control and inversion at the level of probability measures, substantially broadening their role in scientific and engineering applications.

Zoom Meeting ID： 927 8056 1489

Password：0900

Link: https://purdue-edu.zoom.us/j/92780561489?pwd=aXl3cy9Nd1Z5SnJhOW5Id2JDNzRBQT09