Why generative AI is turning back to Langevin diffusions
What do the movements of a single particle and the generation of synthetic data have in common?
For Anna Korba, researcher at ENSAE Paris and speaker at this year’s Hi! PARIS Summer School, the connection runs deep, and it may change how we understand some of today’s most powerful generative models.
At the heart of her work is a concept that dates back to early physics: Langevin diffusions. Originally designed to describe the motion of particles under both attraction and randomness, these models have found new life in machine learning, particularly in the design and analysis of diffusion-based generative systems.
Key Takeaways
- Langevin diffusions are gaining new relevance in machine learning, mainly in how we sample from complex probability distributions.
- Generative models are often evaluated on narrow benchmarks, but their usefulness extends far beyond visual content, into science, engineering, and industry.
- Classical MCMC methods, long considered inefficient, are evolving and being reintegrated into the architecture of generative models.
- A major research challenge today is understanding how generative models, especially diffusion-based ones, actually capture the structure of data.
- Connecting physical intuitions with deep learning could open a better understanding of model dynamics and lead to more robust generative systems.
A quiet comeback for Langevin diffusions
In classical physics, Langevin diffusions help explain how particles are drawn to low-energy states while still subject to random fluctuations. In today’s machine learning landscape, they play a very different role, helping models sample from complex probability distributions by nudging particles toward areas of high density.
These ideas were once the domain of physics and applied mathematics. But as Anna pointed out, that boundary is fading. “It’s striking how two fields that used to be separate are now deeply interconnected,” she said. “Old concepts are coming back with new meaning.”
Why generative models matter beyond images
Korba’s talk also questioned the standard benchmarks used to evaluate generative models. While much of the academic literature highlights their ability to produce images of faces, animals, or artwork, she noted that the real strength of these models lies elsewhere.
Their ability to generate realistic, structured data is increasingly relevant in fields like healthcare, climate science, and engineering. “They’re useful in far more places than where they’re currently tested,” she explained. “People use them everywhere, in industry and in research.”
Anna Korba at the Hi! PARIS Summer School 2025
Rethinking what MCMC methods can do
Another part of Anna’s research focuses on Markov Chain Monte Carlo (MCMC) methods, a class of algorithms often considered too slow or computationally heavy. But that view, she argues, is outdated. Thanks to recent progress in both theory and implementation, these methods are regaining relevance, particularly in generative modeling.
“There’s been a lot of progress that people don’t always see,” she said. “And those advances are already being integrated into newer models.”
A call to understand what’s under the hood
Despite the growing popularity of generative models, we still understand surprisingly little about how they learn. What conditions allow them to capture meaningful structure in data? How do choices in architecture, training, or dataset size influence their behavior?
Anna Korba is especially interested in how these dynamics open out in diffusion models, which are now among the most widely used in AI. “It’s still unclear how they actually capture the structure of the data,” she noted. “Understanding their inner dynamics, and how they connect back to ideas like Langevin diffusions, could help us design better tools.”