Unifying Generative Models with Path Integrals
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Computer Science > Machine Learning
Title:Unifying Generative Models with Path Integrals
Abstract: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.
| Comments: | 51 pages, 4 figures, 4 tables |
| Subjects: | Machine Learning (cs.LG); High Energy Physics - Phenomenology (hep-ph); Machine Learning (stat.ML) |
| Report number: | TIF-UNIMI-2026-11 |
| Cite as: | arXiv:2608.12438 [cs.LG] |
| (or arXiv:2608.12438v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.12438
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Ramon Winterhalder [view email][v1] Wed, 12 Aug 2026 14:52:25 UTC (194 KB)
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