# Unifying Generative Models with Path Integrals

arXiv: https://arxiv.org/abs/2608.12438 · HTML: https://mlsanity.com/paper/2608.12438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
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- First posted on arXiv 12 Aug 2026.

## Abstract (arXiv)

We formulate generative modeling as a path integral in which flow-based, diffusion-based, variational, and adversarial models arise as different evaluation principles for a single master action. Its Martin-Siggia-Rose-Janssen-de~Dominicis (MSRJD) form separates free from interacting probability flows and opens them to diagrammatic perturbation theory. The expansion yields a one-loop correction to deterministic samplers at no stochastic-sampling cost, which we validate on solvable and nonlinear drifts, where it reduces a 53 % tree-level error to 1.6 %. Imperfect learned scores enter as insertions and yield a response-weighted score-matching objective, and symmetry-equivariant drift design becomes an operator expansion with EFT power counting.