Generative models and theoretical physics

This thesis develops symmetry-aware generative models for lattice quantum field theory and, conversely, uses physics to inform generative modeling methods.
We introduce fully equivariant continuous normalizing flows that learn invertible deformations with tractable Jacobians, achieving state-of-the-art sampling performance for the two-dimensional scalar phi^4 theory.
We demonstrate transfer across lattice sizes and conditioning on theory parameters, enabling fast scans and studies near phase transitions.
We extend continuous flows to non-Abelian gauge theories by constructing gauge-equivariant vector fields on matrix Lie groups, including SU(2) and SU(3).
Key technical contributions are vector fields with efficient divergence computation as well as an adaptation of the adjoint-sensitivity method for Lie-group ODE solvers, enabling memory-efficient training with arbitrary architectures.
The resulting models achieve state-of-the-art sampling efficiency for two-dimensional lattice gauge theories and significantly broaden the applicability of flow-based methods in first-principles simulations.
Turning to diffusion-based generative models, we propose Generative Unified Diffusion (GUD), which unifies diffusion and autoregressive generation via explicit choices of basis, prior, and component-wise noising schedules.
GUD clarifies how standard diffusion models work and exposes a continuum between diffusion and autoregressive generation.
Together, these contributions establish a bidirectional bridge between theoretical physics and generative modeling and chart a path toward scalable, symmetry-aware samplers for large-scale lattice simulations.