Theory and Algorithms for Discrete Generative Modeling

Discrete generative modeling is essential for learning complex distributions over structured data
such as text, graphs, and biological sequences. Developing and understanding models for dis-
crete spaces is therefore a key challenge in modern machine learning, with broad implications
for both theory and applications.
The PhD project focuses on the theoretical foundations and algorithmic design of discrete gener-
ative models, situated at the intersection of stochastic processes, probability theory, and machine
learning.
The PhD candidate will investigate continuous-time Markov chains (CTMCs) and jump-diffusion
processes for generative tasks. A core objective is to overcome the “factorization trap” present
in current discrete flow matching models by exploring alternative combinatorial and geometric
structures on the space of probability measures. This will require investigating combinatorial
and geometric structures on probability spaces that go beyond classical Wasserstein geometry.
The candidate will work both on the theoretical aspects and on the implementation of novel
architectures, including hybrid jump-diffusion flows in token embedding spaces.

INSA Lyon is a French engineering school with a strong research environment in science, technology, and applied mathematics. The PhD will be hosted at the Institut Camille Jordan, a joint CNRS mathematics laboratory covering both pure and applied mathematics. The laboratory offers a particularly suitable environment for research at the interface of probability, stochastic processes, numerical methods, and machine learning.

I am looking for a highly motivated candidate with:
- A Master’s degree in Mathematics, Computer Science, or a closely related field.
- A strong background in probability theory and stochastic processes is a plus.
- Interest in the mathematics of machine learning and generative modeling.
- Programming experience; knowledge of Python and frameworks such as PyTorch is a plus.